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SEQUENCES AND SERIES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSEQUENCES AND SERIES3 Marks
Question
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.
✓

Answer

Total letters in the first set = 4, Total letters in the second set = $4^2$ = 16Total letters in the third set $= 4^3 = 64$
$\therefore$ Sequence of letters is 4, 16, 64, ………. in G.P.
Here a = 4, $r = \frac { 16 } { 4 } = 4$ and n = 8
$\therefore \quad S _ { n } = \frac { a \left( r ^ { n } - 1 \right) } { r - 1 }$
$= \frac { 4 \left( 4 ^ { 8 } - 1 \right) } { 8 - 1 }$
$= \frac { 4 } { 3 } ( 65536 - 1 )$
$= \frac { 4 } { 3 } \times 65535 = 87380$
Hence, the total number of letters mailed = 87380
The amount of postage on each letter = 50 paise
Therefore total amount spent on postage = $87380 \times 0.50$ = Rs. 43690.

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