Question

Deposits are made in a geometric progression. Given that 4th and the 7th deposits are 24000 and 192000 respectively. Calculate
1- The 10th deposits
2- The sum of the first 10 deposits

Answer 1

let $a=$ first deposit, $r=$ common ratio

$4th$ deposit correspond to $ar^{3}$ and $7th$ correspond to $ar^{6}$

$ar^{3}=24000$ and $ar^{6}=192000$

$a=24000/r^{3}$ and $a=192000/r^{6}$

$24000/r^{3}=192000/r^{6}$

$r^{3}=8, r=8^{1/3}=2$

$a=24000/8=3000$

1) the tenth deposit $=ar^{9} = 3000\times 2^{9}=1,536,000$

2) sum of the first 10 deposits = $a(r^{n}-1)/(r-1)$ $=3000(2^{10}-1)/(2-1)= 3,069,000$