Question

A person writes a letter 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 it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.

Answer 1

Total letters in the first set = 4

Total letters in the second set $=4^2=16$

Total letters in the third set $=4^3=64$

So the sequence of letters is 4, 16, 64, ....

Here $a=4$, $r=\frac{16}{4}=4$ and $n=8$

Now, $S_n=\frac{a(r^n-1)}{r-1}$

$\therefore S_8=\frac{4(4^8-1)}{4-1}=\frac{4}{3}(65536-1)$

$=\frac{4}{3}\times 65535=87380$

Since amount of postage on each letter is 50 paise,

$\therefore$ Toal amount spent on postage

$=87380\times \frac{50}{100}=Rs.Rs.43690$