Rohit 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 the instructions that they move the chain similarly. Assuming that the chain is not broken and that it costs ₹ 10 to mail one letter, determine the amount spent on postage when the fourth set of letters is mailed.

Rohit writes a letter to four of his friends, and each of them copies the letter and mail it to four different persons and the chain continues. Thus, the above sequence is :

4, 16, 64, …….

The above sequence is a G.P., with first term (a) = 4 and r = 4.

By formula,

Sum of G.P. = $\dfrac{a(r^n - 1)}{(r - 1)}$

Thus,

$S_4 = \dfrac{4 \times (4^4 - 1)}{4 - 1} \\[1em] = \dfrac{4 \times (256 - 1)}{3} \\[1em] = \dfrac{4 \times 255}{3} \\[1em] = 4 \times 85 \\[1em] = 340.$

Thus, total 340 letters are mailed till fourth set.

If, it costs ₹ 10 to mail one letter.

Total cost = No. of letters × 10 = 340 × ₹ 10 = ₹ 3,400.

Hence, amount spent on postage = ₹ 3,400.