Given a geometric sequence that starts with the terms 3,−6,12,−24,..., calculate the sum of the first fifteen terms. A 98,301 B 32,769 C −16,383 D −14,348,906

B 32,769

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1)/(r - 1)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

a = 3

r = - 6/3 = - 2

n = 12

Therefore, the sum of the first 15 terms, S15 is

S15 = (3 × - 2^(15) - 1)/- 2 - 1

S15 = (3 × -32769)/- 3

S15 = -98307/- 3

S15 = 32769

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

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