This page contains peer generated solutions and error explanations to OFSA questions. As you read or view the solutions, be critical: check for accuracy, but also for more efficient solution strategies. If you have a better method or different idea/answer, post a discussion and monitor the responses.

Quick Directions

Post answers, solutions and error explanations to each OFSA question below.

For each "distractor" or incorrect answer choice, explain the error that would lead to that incorrect answer choice.

You may either do the above in typed format or using a pencast.

Separate each question with a section bar.

After each solution, provide a hyperlink back to the corresponding OFSA page.

Question 1 What's the interval over which this infinite series converges?

Solution 1

4 < x - 3
x > 7

x - 3 < -4
x < -1 Answer: A

Error Explanation 1
A) x > -7 or x < -1
B) x > -7
C) x < -1
D) -1 < x < 1

A: Correct
B: It's not just greater than 7; must check other side.
C: It's not just less than -1; must check other side.
D: This is just the concept of the magnitude of the ratio r must be between -1 and 1.

Click here to return to OFSA. Question 2 What's the explicit geometric rule for 10, -5, 2.5, -1.25, ... ?

Solution 2

Answer: B

Error Explanation 2
A)

B)

C)

D)

A: This one doesn't have a negative in front of the ratio.
B: Correct
C: This one doesn't have the exponent of (n-1). If this is true, it would start at n=0 for the first term to be 10.
D: The ratio is wrong in this choice.

Click here to return to OFSA. Question 3 Given the rule of:

Find the sum of the first 11 terms (calc. okay).

Solution 3
Type in your calculator:
TI 83/84 - sum(seq(3^x+(-2)^x, x, 1, 11))
TI 89 - F3, 4, then S (3^x+(-2)^x, x, 1, 11)
You get out the answer 264,353. Answer: B

Error Explanation 3
A) 175,009
B) 264,353
C) 2,049
D) 125,635

A: When you just plug in 11 for the rule, you get this number, which is just the 11th term.
B: Correct
C: You get this answer if you try to use a partial sum of a geometric sequence rule, by using the first term as 3, the ratio as -2, and the number of terms as 11.
D: Random answer.

Click here to return to OFSA. Question 4 Find the nth term of the sequence
1, -8, 27, -64...

Solution 4
Note that each term is the cube of a natural number and that the signs alternated.

The formula

seems the appropriate choice, but let’s check.
Thus, all is well and the solution is

Error Explanation 4
a) sign of even number of n is incorrect
b) sign of odd number of n is incorrect
c) correct
d) it will not work after first one because it is not square.
e) same as d) that it will not work on after first one because it is not square.
Click here to return to OFSA. Question 5 Find the 4th term of the recursive sequence

where a1=4

Solution 5

a1 = 4, gives

Error Explanation 5
a) answer is 134 from above, so incorrect
b) answer is 134 from above, so incorrect
c) answer is 134 from above, so incorrect
d) answer is 134 from above, so incorrect
e) correct because none of answers are correct
Click here to return to OFSA. Question 6 Compute the sum

Solution 6

Error Explanation 6
a) added wrong
b) added wrong
c) correct
d) denominator is correct, but numerator added wrong
e) c is answer, so this is wrong
Click here to return to OFSA. Question 7 Compute the sum

Solution 7
This is geometric with common ration r = -x. Thus, the sum of these 6 terms is

Error Explanation 7
a) denominator is correct, but numerator added wrong
b) sign and numerator added wrong
c) sign of numerator is not +x^6
d) correct
e) There is no a in this question...
Click here to return to OFSA. Question 8 Find the sum of the infinite series

Solution 8
This is geometric with common ration r = 1/2. Because −1 < r < 1, the series converges and

Error Explanation 8
a) forget about denominator, so incorrect
b) add 1 to a)`s answer, but still incorrect
c) correct
d) added denominator instead of subtract them(1+r)
e) answer is c, so this is incorrect
Click here to return to OFSA. Question 9 Solution 9

Error Explanation 9
B) Must remember to subtract 1 from the number of terms to get the right answer.
C) Important to remember that when using rule to subtract 1 from 200 not add.
D) Be sure to use the correct distance between consecutive terms.

Click here to return to OFSA. Question 10 Solution 10
Because
S = 3 + 5 + 7 + · · · + 101,
we have a = 3 and d = 2, so

Use an = 101 to determine the number of terms.

->1 + 2n = 101
->2n = 100
->n = 50
Thus, there are 50 terms. We can now use

S = 2600 (B) Error Explanation 10
A) Make sure to use correct distance between terms.
B) ~
C) Make sure to find the number of terms located in the sequence first.
D) Make sure to find the number of terms located in the sequence first.

Click here to return to OFSA. Question 11 Solution 11

(A) Error Explanation 11
A) ~
B) Make sure you are using the correct equation and remember it is geometric.
C) Make sure not to add the ration when calculating the sum.
D) Place corrects signs in each area of the equation as to not mess you up.

Click here to return to OFSA. Question 12 Solution 12 Error Explanation 12
Click here to return to OFSA. Question 13 Solution 13 Error Explanation 13
Click here to return to OFSA. Question 14 Solution 14 Error Explanation 14
Click here to return to OFSA. Question 15 Solution 15 Error Explanation 15
Click here to return to OFSA. Question 16 Solution 16 Error Explanation 16
Click here to return to OFSA. Question 17 Solution 17 Error Explanation 17
Click here to return to OFSA. Question 18 Solution 18 Error Explanation 18
Click here to return to OFSA. Question 19 Solution 19 Error Explanation 19
Click here to return to OFSA. Question 20 Solution 20 Error Explanation 20
Click here to return to OFSA. Question 21 Solution 21 Error Explanation 21
Click here to return to OFSA. Question 22 Solution 22 Error Explanation 22
Click here to return to OFSA. Question 23 Solution 23 Error Explanation 23
Click here to return to OFSA. Question 24 Solution 24 Error Explanation 24
Click here to return to OFSA. Question 25

OFSA SOLUTIONS for Sequences and SeriesThis page contains peer generated solutions and error explanations to OFSA questions. As you read or view the solutions, be critical: check for accuracy, but also for more efficient solution strategies. If you have a better method or different idea/answer, post a discussion and monitor the responses.

Quick DirectionsQuestion 1What's the interval over which this infinite series converges?Solution 14 < x - 3

x > 7

x - 3 < -4

x < -1

Answer: AError Explanation 1A) x > -7 or x < -1

B) x > -7

C) x < -1

D) -1 < x < 1

A: Correct

B: It's not just greater than 7; must check other side.

C: It's not just less than -1; must check other side.

D: This is just the concept of the magnitude of the ratio

rmust be between -1 and 1.Click here to return to OFSA.

Question 2What's the explicit geometric rule for 10, -5, 2.5, -1.25, ... ?Solution 2Answer: BError Explanation 2A)

B)

C)

D)

A: This one doesn't have a negative in front of the ratio.

B: Correct

C: This one doesn't have the exponent of (n-1). If this is true, it would start at n=0 for the first term to be 10.

D: The ratio is wrong in this choice.

Click here to return to OFSA.

Question 3Given the rule of:Find the sum of the first 11 terms (calc. okay).Solution 3Type in your calculator:

TI 83/84 - sum(seq(3^x+(-2)^x, x, 1, 11))

TI 89 - F3, 4, then S (3^x+(-2)^x, x, 1, 11)

You get out the answer 264,353.

Answer: BError Explanation 3A) 175,009

B) 264,353

C) 2,049

D) 125,635

A: When you just plug in 11 for the rule, you get this number, which is just the 11th term.

B: Correct

C: You get this answer if you try to use a partial sum of a geometric sequence rule, by using the first term as 3, the ratio as -2, and the number of terms as 11.

D: Random answer.

Click here to return to OFSA.

Question 4Find the nth term of the sequence1, -8, 27, -64...

Solution 4Note that each term is the cube of a natural number and that the signs alternated.

The formula

seems the appropriate choice, but let’s check.

Thus, all is well and the solution is

Error Explanation 4a) sign of even number of n is incorrect

b) sign of odd number of n is incorrect

c) correct

d) it will not work after first one because it is not square.

e) same as d) that it will not work on after first one because it is not square.

Click here to return to OFSA.

Question 5Find the 4th term of the recursive sequencewhere a1=4Solution 5a1 = 4, gives

Error Explanation 5a) answer is 134 from above, so incorrect

b) answer is 134 from above, so incorrect

c) answer is 134 from above, so incorrect

d) answer is 134 from above, so incorrect

e) correct because none of answers are correct

Click here to return to OFSA.

Question 6Compute the sumSolution 6Error Explanation 6a) added wrong

b) added wrong

c) correct

d) denominator is correct, but numerator added wrong

e) c is answer, so this is wrong

Click here to return to OFSA.

Question 7Compute the sumSolution 7This is geometric with common ration r = -x. Thus, the sum of these 6 terms is

Error Explanation 7a) denominator is correct, but numerator added wrong

b) sign and numerator added wrong

c) sign of numerator is not +x^6

d) correct

e) There is no a in this question...

Click here to return to OFSA.

Question 8Find the sum of the infinite seriesSolution 8This is geometric with common ration r = 1/2. Because −1 < r < 1, the series converges and

Error Explanation 8a) forget about denominator, so incorrect

b) add 1 to a)`s answer, but still incorrect

c) correct

d) added denominator instead of subtract them(1+r)

e) answer is c, so this is incorrect

Click here to return to OFSA.

Question 9Solution 9Error Explanation 9B) Must remember to subtract 1 from the number of terms to get the right answer.

C) Important to remember that when using rule to subtract 1 from 200 not add.

D) Be sure to use the correct distance between consecutive terms.

Click here to return to OFSA.

Question 10Solution 10Because

S = 3 + 5 + 7 + · · · + 101,

we have a = 3 and d = 2, so

Use an = 101 to determine the number of terms.

->1 + 2n = 101

->2n = 100

->n = 50

Thus, there are 50 terms. We can now use

S = 2600 (B)

Error Explanation 10A) Make sure to use correct distance between terms.

B) ~

C) Make sure to find the number of terms located in the sequence first.

D) Make sure to find the number of terms located in the sequence first.

Click here to return to OFSA.

Question 11Solution 11(A)Error Explanation 11A) ~

B) Make sure you are using the correct equation and remember it is geometric.

C) Make sure not to add the ration when calculating the sum.

D) Place corrects signs in each area of the equation as to not mess you up.

Click here to return to OFSA.

Question 12Solution 12Error Explanation 12Click here to return to OFSA.

Question 13Solution 13Error Explanation 13Click here to return to OFSA.

Question 14Solution 14Error Explanation 14Click here to return to OFSA.

Question 15Solution 15Error Explanation 15Click here to return to OFSA.

Question 16Solution 16Error Explanation 16Click here to return to OFSA.

Question 17Solution 17Error Explanation 17Click here to return to OFSA.

Question 18Solution 18Error Explanation 18Click here to return to OFSA.

Question 19Solution 19Error Explanation 19Click here to return to OFSA.

Question 20Solution 20Error Explanation 20Click here to return to OFSA.

Question 21Solution 21Error Explanation 21Click here to return to OFSA.

Question 22Solution 22Error Explanation 22Click here to return to OFSA.

Question 23Solution 23Error Explanation 23Click here to return to OFSA.

Question 24Solution 24Error Explanation 24Click here to return to OFSA.

Question 25