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.

Explanation

Number of letters in the 1st set=4 ( These are letters sent by Dipesh )
Number of letters in the 2nd set `4+4+4+4=16`
Number of letters in the 3rd set ` =4+4+4+4+"…."+16 " terms " =64`
` " " vdots " " vdots " " vdots " " vdots `
The number of letters sent in the 1st set, 2nd set, 3rd set,`"...."` are respectively `4,16,64,"...."` which is a GP with `a=4`
`r=(16)/(4)=(64)/(16)=4`
`therefore` The number of letters in all the first 8 sets
`=(4(4^(8)-1))/(4-1)=87380`
`therefore` Total money spent on letters `=87380xx(25)(100)=21845`