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# In the series 2,10,50 ------ the number of terms required to make a sum of 7812 is

$\begin{array}{1 1} 5 \\ 6\\ 10 \\ 70 \end{array}$

Explanation : 2,10,50 ------ is a with a=2 , r=5
$S_{n}=\frac{a(r^n-1)}{r-1}=\frac{2(5^n-1)}{5-1}=7812$
$5^n=(7812*2)+1=15625=5^6$
$n=6.$