Question

A person saved every year half as much he saved the previous year. If he totally saved Rs. 19375 in 5 years, how much did he save the first year?

Answer 1

Given : $r=\frac{1}{2},n=5,S_5=19375$

To find $a$

$S_n=a\left(\frac{1-r^n}{1-r}\right)$

$⟹S_5=a\left(\frac{1-r^5}{1-r}\right)$

$⟹19375=a\left(\frac{1-(\frac{1}{2}{)}^5}{1-\frac{1}{2}}\right)$

$⟹19375=a\left(\frac{1-\left(\frac{1}{32}\right)}{1-\frac{1}{2}}\right)$

$⟹19375=a\left(\frac{\frac{31}{32}}{\frac{1}{2}}\right)=a\left(\frac{31}{16}\right)$

$⟹a=\frac{19375\times 16}{31}$

$=625\times 16=10000$

$\therefore a=10000$

Hence, the person saved Rs. $10,000$.