# Calculus

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If S1 = 0.7 and S2 = 2.1 in geometric series, what would the sum of the first 12 terms in the series be?

I tried doing this, and I got 1.16 or something :S How exactly do I do this? Please tell me what formula to use. I was using the Sn = a(rn-1)/r-1

• Calculus -

The geometric series up to the nth term is generally represented by the formula:
S(n)=a + ar + ar^2 + ar^3 .... + ar^(n-1)

Therefore
S(1)=a=0.7
S(2)=a+ar=a(1+r)=0.7*(1+2)
Therefore r=2

The formula for calculating the first n terms is
S(n)=a(r^n-1)/(r-1)
for n=12,
=0.7*(2^12-1)/(2-1)
You calculator should tell you that S(12) is below 3000.

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