Question

What is the common difference between successive terms in the sequence?

9, 2.5, –4, –10.5, –17, ...

–11.5
–6.5
6.5
11.5Martina opens a savings account with an initial deposit and makes no other deposits or withdrawals. She earns interest on her initial deposit. The total amount of money in her savings account at the end of each year is represented by the sequence shown.

100, 105, 110.25, ...
Which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year?

f(n + 1) = f(n) + 5
f(n + 1) = 5f(n)
f(n + 1) = 1.05f(n)
f(n + 1) = 0.05f(n) What is the common ratio between successive terms in the sequence?

27, 9, 3, 1, one-third, one-ninth, StartFraction 1 over 27 EndFraction, ...

–3
–

3A sequence is defined by the recursive function f(n + 1) = –10f(n).

If f(1) = 1, what is f(3)?

3
–30
100
–1,000Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1?

5,–1, –7, –13, –19, ...

f(n + 1) = f(n) + 6
f(n) = f(n +1) – 6
f(n +1) = f(n) – 6
f(n +1) = –6f(n)What is the common difference between successive terms in the sequence?

0.36, 0.26, 0.16, 0.06, –0.04, –0.14, ...

–0.1
–0.01
0.01
0.1What is the common ratio between successive terms in the sequence?

1.5, 1.2, 0.96, 0.768, …

–0.8
–0.3
0.3
0.8Zina spends 1.5 hours setting up her sewing machine and making one hat. The total amount of time spent making hats can be represented by the sequence below.

1.5, 2.25, 3.0, 3.75, ...
Which recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously?

f(n + 1) = f(n) + 1.5
f(n + 1) = f(n) + 0.75
f(n + 1) = one-halff(n)
f(n + 1) = three-halvesf(n)A sequence is defined recursively using the equation . If f(1)=100, what is f(6)?

52
60
68
92What is the common ratio between successive terms in the sequence?

2, –4, 8, –16, 32, –64, ...

–2
–6
6
2

Answer 1

1) Common difference for 9, 2.5, –4, –10.5, –17: −6.5

2) Martina’s recursive interest formula: f(n+1) = 1.05 f(n)

3) Common ratio for 27, 9, 3, 1, 1/3, …: 1/3

4) If f(n+1) = −10 f(n) and f(1)=1, then f(3) = 100

5) Recursive formula for 5, −1, −7, −13, …: f(n+1) = f(n) − 6

6) Common difference for 0.36, 0.26, 0.16, …: −0.1

7) Common ratio for 1.5, 1.2, 0.96, 0.768, …: 0.8

8) Zina’s recursive formula: f(n+1) = f(n) + 0.75

9) If the recursion is f(n+1) = f(n) − 8 with f(1)=100, then f(6) = 100 − 5·8 = 60

10) Common ratio for 2, −4, 8, −16, …: −2