Find the sum of the first seven terms of the geometric series 2 - 10 + 50 +

Question

A. 23405

B. 26042

C. 28406

D. 29583

Answer 1

The answer is B. 26,042

The formule is S(n) = a(1)[(1 - r^n)]/(1 - r)]

Identify the initial term a(1) which is 2, the common ratio r which is -5 and the number of terms n which is 7.

S = 2[1 -(-5)^7]/[1 - (-5)]

S = 2(1 + 78,125)/(1 + 5)

s = 2(78126)/6

S = 26,042

Since there are only 7 terms we can very easily check by what I call 'brute force' and add the terms one at a time. (Not recommended when there are a very large number of terms.)

S = 2 - 10 + 50 - 250 + 1250 - 6250 + 31250 = 26,042

Note that because r is negative the terms alternate between positive and negative.

Answer 2

S₅ = 2(1 - (-2)⁵ / (1 - (-2)) A formula!