Regents Exam Questions F.IF.A.3: Sequences2aPage 1

Name: ______

1A sequence of blocks is shown in the diagram below.

This sequence can be defined by the recursive function and . Assuming the pattern continues, how many blocks will there be when ?

1) / 13
2) / 21
3) / 28
4) / 36

2In a sequence, the first term is 4 and the common difference is 3. The fifth term of this sequence is

1) /
2) /
3) / 16
4) / 19

3What is the fifteenth term of the sequence ?

1) /
2) /
3) / 81,920
4) / 327,680

4An arithmetic sequence has a first term of 10 and a sixth term of 40. What is the 20th term of this sequence?

1) / 105
2) / 110
3) / 124
4) / 130

5On the main floor of the Kodak Hall at the Eastman Theater, the number of seats per row increases at a constant rate. Steven counts 31 seats in row 3 and 37 seats in row 6. How many seats are there in row 20?

1) / 65
2) / 67
3) / 69
4) / 71

6What is the fifteenth term of the geometric sequence ?

1) /
2) /
3) /
4) /

7The first four terms of the sequence with and are

1) /
2) /
3) /
4) /

8If and , what is the value of ?

1) / 5
2) / 20
3) / 120
4) / 720

9Given the function defined by the following:

Which set could represent the range of the function?

1) /
2) /
3) /
4) /

10The first four terms of the sequence defined by and are

1) /
2) /
3) /
4) /

11What is the fourth term of the sequence defined by

1) /
2) /
3) /
4) /

12What is the third term of the recursive sequence below?

1) /
2) /
3) /
4) /

13If and , then

1) /
2) / 11
3) / 21
4) / 43

14If a sequence is defined recursively by and for , then is equal to

1) / 1
2) /
3) / 5
4) / 17

15The eighth and tenth terms of a sequence are 64 and 100. If the sequence is either arithmetic or geometric, the ninth term can not be

1) /
2) /
3) / 80
4) / 82

16Find the third term in the recursive sequence , where .

17Write the first five terms of the recursive sequence defined below.

18Find the first four terms of the recursive sequence defined below.

19Use the recursive sequence defined below to express the next three terms as fractions reduced to lowest terms.

20The recursive formula to describe a sequence is shown below.

State the first four terms of this sequence. Can this sequence be represented using an explicit geometric formula? Justify your answer.

Regents Exam Questions F.IF.A.3: Sequences2a

1ANS:3

1, 3, 6, 10, 15, 21, 28, ...

REF:081715ai

2ANS:3

REF:061613ai

3ANS:3

REF:011105a2

4ANS:3

REF:081510a2

5ANS:1

REF:061807ai

6ANS:1

REF:061109a2

7ANS:2

REF:081608a2

8ANS:3

, , ,

REF:061824ai

9ANS:2

; ; ;

REF:061718ai

10ANS:1REF:081520a2

11ANS:3

REF:061512a2

12ANS:1

REF:011623a2

13ANS:4

REF:081424ai

14ANS:3

REF:011520ai

15ANS:1

REF:011714aii

16ANS:

. . .

REF:061233a2

17ANS:

REF:081832ai

18ANS:

REF:fall0934a2

19ANS:

REF:011537a2

20ANS:

; No, because there is no common ratio:

REF:061830aii