Question

Find the sum of the first 6 terms of geometric series 2-10+50+.....

Answer 1

Answer:   -5208

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Work Shown:

term1 = 2

term2 = -10

term3 = 50

term4 = -250

term5 = 1250

term6 = -6250

Each new term is found by multiplying the previous term by -5

Add up the terms

2 + (-10) + 50 + (-250) + 1250 + (-6250) = -5208

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A shortcut is to use a = 2, r = -5 and n = 6 in the formula below

Sn = a*(1-r^n)/(1-r)

S6 = 2*(1-(-5)^6)/(1-(-5))

S6 = 2*(1-15625)/(1+5)

S6 = 2*(-15624)/6

S6 = -31248/6

S6 = -5208