5.9.1 Finding the formula for a finite geometric series

1. Expand the finite geometric series to show few terms, including the last.
2. Multiply by the common ratio, r, on both sides.
3. Subtract the two series, in such a way that it helps to collapse only the first and last term.
4. Then solve for Sn

S_n = a + ar¹ + ar² +……. + ar^{n – 1}

rS_n = r (a + ar¹ + ar² +……. + arn – 1)

S_n – rS_n = a – arⁿ

S_n = a (1 – rⁿ)/1 – r

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