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 = \(\frac{170}{256}\)