Question

A person writes a letter to four of his friends. He asked each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that is costs $50$ paise to mail one letter. Find the amount spent on the postage when $8^{th}$ set of letter is mailed.

Answer 1

Number of letters

$1$set$=4$

$2$nd set $=4\times 4=16$

$3$rd set $=16\times 4=64$

Hence, sequence is $4,16,64,...$

This is a G.P whose common ration, $r=4$

and, first term, $a=4$

we need to find number of total letters mailed upto $8$th set of letters i.e., $s_8$

for $r>1$

$s_n=\frac{a(r^n-1)}{r-1}$

$s_8=\frac{4(4^8-1)}{3}=\frac{4(65536-1)}{3}=4\left(21845\right)$

$=87380$

Hence, total number of letters posted after $8$th set is $87380$

Hence amount spent on postage

$=\frac{50}{100}\times 87380$

$=$Rs. $43690$.