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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