Worksheet 50 - Geometric Sequences.ks-ia2

Math Analysis Honors - Worksheet 50

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Geometric Sequences

Determine if the sequence is geometric. If it is, find the common ratio, the explicit formula, and the recursive formula.

1) -4, 20, -100, 500, ...

2) 4, 20, 100, 500, ...

3) 4, 24, 144, 864, ...

4) 3, -12, 48, -192, ...

Given the explicit formula for a geometric sequence find the term named in the problem and the recursive formula.

5) a = 3 3n - 1 n Find a 9

6) a = -2 4n - 1 n Find a 10

7) a = -3 2n - 1 n Find a 12

8) a = -(-3)n - 1 n Find a 11

Given the first term and the common ratio of a geometric sequence find the term named in the problem, the explicit formula, and the recursive formula.

9) a = 1, r = -2 1 Find a 10

10) a = 1, r = 2 1 Find a 12

11) a = 1, r = 3 1 Find a 9

12) a = 2, r = -3 1 Find a 9

Given a term in a geometric sequence and the common ratio find the explicit formula.

13) a = -36, r = 6 3

14) a = 64, r = 2 6

Determine the number of terms n in each arithmetic series.

15) 24 + 34 + 44 + 54..., S = 2166 n

16) (-6) + (-4) + (-2) + 0..., S = 0 n

Evaluate each arithmetic series described.

17) (-7) + (-5) + (-3) + (-1)..., n = 14

18) 33 + 39 + 45 + 51..., n = 14

Evaluate each series.

7

19) (2m2 - 4)

m = 2

12

20) n

n = 0

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Worksheet by Kuta Software LLC

1) Common Ratio: r = -5

Explicit: a = -4 (-5)n - 1 n

Recursive: a = a -5

n

n - 1

a = -4 1

4) Common Ratio: r = -4

Explicit: a = 3 (-4)n - 1 n

Recursive: a = a -4

n

n - 1

a =3 1

7) a = -6144 12

Recursive: a = a 2

n

n - 1

a = -3 1

Answers to

2) Common Ratio: r = 5

Explicit: a = 4 5n - 1 n

Recursive: a = a 5

n

n - 1

a =4 1

5) a = 19683 9

Recursive: a = a 3

n

n - 1

a =3 1

8) a = -59049 11

Recursive: a = a -3

n

n - 1

a = -1 1

10) a = 2048 12

11) a = 6561 9

Explicit: a = 2n - 1 n

Explicit: a = 3n - 1 n

Recursive: a = a 2

n

n - 1

Recursive: a = a 3

n

n - 1

a =1 1

a =1 1

13) a = -6n - 1 n

14) a = 2 2n - 1 n

15) 19

17) 84

18) 1008

19) 254

3) Common Ratio: r = 6

Explicit: a = 4 6n - 1 n

Recursive: a = a 6

n

n - 1

a =4 1

6) a = -524288 10

Recursive: a = a 4

n

n - 1

a = -2 1

9) a = -512 10

Explicit: a = (-2)n - 1 n

Recursive: a = a -2

n

n - 1

a =1 1

12) a = 13122 9

Explicit: a = 2 (-3)n - 1 n

Recursive: a = a -3

n

n - 1

a =2 1

16) 7

20) 78

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Worksheet by Kuta Software LLC

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