A person writes a letter to four of his friends.
Question:

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

Solution:

The numbers of letters mailed forms a G.P.: $4,4^{2}, \ldots 4^{8}$

First term = 4

Common ratio = 4

Number of terms = 8

It is known that the sum of n terms of a G.P. is given by

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

$\therefore S_{8}=\frac{4\left(4^{8}-1\right)}{4-1}=\frac{4(65536-1)}{3}=\frac{4(65535)}{3}=4(21845)=87380$

It is given that the cost to mail one letter is 50 paisa.

$\therefore$ Cost of mailing 87380 letters $=$ Rs $87380 \times \frac{50}{100}=$ Rs 43690

Thus, the amount spent when $8^{\text {th }}$ set of letter is mailed is Rs 43690 .

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