Question

Kumar 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 instruction that they continue the process similarly. Assuming that the process is unaltered and it costs ₹ 2 to mail one letter, find the amount spent on postage when 8^th set of letters is mailed

Answer 1

When Kumar writes a letter to his friend. A friend writes a letter to another person.

It forms a G.P.

The G.P. is 4, 16, 64, ...

Here a = 4, r = 4

The last term is 4 (4)^8-1 = 4(4)⁷ 

S₈ = `(4(4^8 - 1))/(4 - 1)`

= `(4(65536 - 1))/3`

= `(4 xx 65535)/3`

= 87380

Cost to mail the letter = ₹ 2 (87380)

= ₹ 174760