# Find the sum of the following infinite geometric series if it exists. (2/5) + (12/25) + (72/125) +...

Find the sum of the following infinite geometric series if it exists. (2/5) + (12/25) + (72/125) +...
 A. 5/12 B. Does not exist C. 5/6 D. 6/5
Which of the following is not a geometric sequence?
 A. 1, 2, 4, 8 B. 3, 1, -1,-3 C. ½, ¼, 1/8, 1/16 D. 216, 72, 24, 8

asked Sep 10, 2014

(1).

The geometric series is (2/5) + (12/25) + (72/125) + · · · · · · · .

To calculate the sum of the infinite geometric series by using formula : S = a1/(1 - r), - 1 < r < 1 ; where a1 = first term and r = common ratio.

a1 = 2/5 and r = a2 / a1 = (12/25) / (2/5) = 6/5 = 1.2.

Since r = 1.2 does not lie in the interval (- 1, 1), the sum of the infinite geometric series does not exist.

The option B is correct.

answered Sep 10, 2014
selected Sep 10, 2014 by tonymate

(2).

The sequence is 1, 2, 4, 8.

First find the ratios of consecutive terms.

2/1 = 4/2 = 8/4 = 2.

The ratios of consecutive terms are the same, so sequence is geometric sequence.

The sequence is 3, 1, - 1, - 3.

First find the ratios of consecutive terms.

1/3 ≠ - 1/1 ≠ (-3)/(-1).

The ratios of consecutive terms are not same, so sequence is not geometric sequence.

The sequence is 1/2, 1/4, 1/8, 1/16.

First find the ratios of consecutive terms.

(1/4) / (1/2) = (1/8) / (1/4) = (1/16) / (1/8) = 1/2.

The ratios of consecutive terms are the same, so sequence is geometric sequence.

The sequence is 216, 72, 24, 8.

First find the ratios of consecutive terms.

72 / 216 = 24 / 72 = 8 / 24 = 1/3.

The ratios of consecutive terms are the same, so sequence is geometric sequence.

The option B is correct.

answered Sep 10, 2014