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 8^th set of letters is mailed.

According to question -

No. of letters in 1st set = 4

No. of letters in 2nd set = 4 × 4 = 16

No. of letters in 3rd set = 16 × 4 = 64

Hence, the sequence is

i.e. 4, 16, 64, …

This is a GP as

(16/4) = 4 & (64/16) = 4

Common ratio(r) = 4

First Term(a) = 4

Total no. of letters mailed upto 8th set is given by putting values of a, r & n(=8) in

(as r>1)

∴

= 4 × 21845

= 87380

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

Given that -

Postage Charge per Letter = 50 paise

Hence, the amount spend on the postage of 8738 letter is

= Rs. [(50/100) × 87380]

= Rs. 43690