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 letter is mailed.

Asked by Pragya Singh | 1 year ago | 138

It’s seen that,

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

Here, first term = 4 and common ratio = 4

And the number of terms = 8

The sum of n terms of a G.P. is given by:

\( s_n=\dfrac{a(r^n-1)}{r-1}\)

\( s_8=\dfrac{4(4^8-1)}{4-1}\)

\(=\dfrac{4(65536-1)}{3}\)

\( =\dfrac{4(65535)}{3}\)

= 4(21845)

= 87380

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

Hence, Cost of mailing 87380 letters = Rs 87380 x (\( \dfrac{50}{100}\)) = Rs 43690 = Rs 43690

Therefore, the amount spent when 8^{th} set of letter is mailed will be Rs 43690.

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