14.2 Practice

14.2 Practice

Find the next three terms in each sequence. Then, tell if the sequence converges or diverges.

1) 2, 6, 18, 54, 162, ...

486, 1458, 4374 (diverges)

2) -1, 2, 7, 14, 23, ...

34, 47, 62 (diverges)

3) -3, 15, -75, 375, -1875, ...

9375, -46875, 234375

4) 2xx, x5x,xx1x0x,x1xx7x, x2x6x,x.x..x

1.11111, 1.111111, 1.1111111 converges to 1.1 or 10/9

Find the first four terms in each sequence, given the explicit formula.

5) a = 5n - 1 n 1, 5, 25, 125

6) a = -12 + 30n n 18, 48, 78, 108

7) a = n2 - 1 n 0, 3, 8, 15

8 8) a =

n n+2

Find the first four terms in each sequence, given the recursive formula.

3 9) a = a +

2 n n - 1 a =0

1

0, 3/2, 3, 9/2

10) a = a ? -5 n n-1 a = -3 1

-3, 15, -75, 375

11) a = a ? 4 n n-1 a = 3 3, 12, 48, 192 1

2 + a

12) a =

n - 1

n

2

a = 10 1

10, 6, 4, 3

Write the explicit formula for each sequence.

13) 4, 20, 100, 500, 2500, ...

a = 4 ? 5

14) 29, 20, 11, 2, -7, ...

a = 38 - 9n

35 15) 1, , 2, , 3, ...

22

16) 2, 5, 10, 17, 26, ...

Write the recursive formula for each sequence.

17) 3, -6, 12, -24, 48, ...

33 3 3 18) -3, - , - , - , - , ...

4 16 64 256

19) -4, -8, -16, -32, -64, ...

33 3 3 20) 3, - , , - , , ...

5 25 125 625

Evaluate each series.

6

S 21) (3k2 - 2) k = 1

8

S 22) (20 - a) a = 2

6

S 23) k(k - 2) k = 1

9

S 24) k2 k = 4

11

S 25) (40 - m) m = 5

Rewrite each series using sigma notation.

27) 4 + 16 + 64 + 256

4

S 26) (3k2 + 3) k = 0

28) 1 + 4 + 9 + 16 + 25

29) 301 + 302 + 303 + 304 + 305 + 306

30) 601 + 602 + 603 + 604

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