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+1 vote
2.2k views
in Geometric Progressions by (15.7k points)

The 2nd and 5th terms of a GP are \(-\frac{1}{2}\) and \(\frac{1}{16}\) respectively. Find the sum of n terms GP up to 8 terms.

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1 Answer

+1 vote
by (15.2k points)

2 nd term = ar2-1 = ar1 

5th term = ar5-1 = ar4 

Dividing the 5th term using the 3rd term

\(\cfrac{ar^4}{ar} = \cfrac{\frac{1}{16}}{\frac{-1}{2}}\)

r3 = \(-\frac{1}{8}\)

\(\therefore\) r = \(-\frac{-1}{2}\)

\(\therefore\) a = 1

Sum of a G.P. series is represented by the formula, Sn\(a \frac{1-r^n}{1-r}\), when |r|<1. 

‘Sn’ represents the sum of the G.P. series up to nth terms, 

‘a’ represents the first term, 

‘r’ represents the common ratio and 

‘n’ represents the number of terms.

n = 8 terms

⇒ Sn = \(\cfrac{1- \frac{1}{256}}{\frac{3}{2}}\)

⇒ Sn = \(\cfrac{\frac{255}{256}}{\frac{3}{2}}\)

∴ Sn = \(\frac{170}{256}\)

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