Question

if the 5th and 12th terms of an A.P are 14 and 35 respectively find the first term and the common diffrnc

Answer 1

$\huge\bf\underline{\underline{Question:}}$

If the 5th and 12th terms of an A.P are 14 and 35 respectively find the first term and the common difference.

$\huge\bf\underline{\underline{Solution:}}$

$a_5 = 14\\a + 4d = 14--(i)\\ \\a_{12}=35\\a+11d=35--(ii)$

${\sf{Now\: we\: need\: to\: solve\: equation \:(i)\: and\: (ii)}}$

${\sf{So\:subtract\: equation\: (i)\:from\:(ii)}}$

${\sf{We\: get,}}$

$7d=21\\ \boxed{\red{d=3}}$

${\sf{put \:in\: equation\:(i)}}$

$a+4(3)=14\\a+12=14$

$\boxed{\red{a=2}}$

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