Q7 In an AP, the first term is -12 and the last term is 40. If the sum of all terms is 196, find the common difference and number of terms.

asked May 12, 2021 39.8k views

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Q7

In an AP, the first term is -12 and the last term is 40. If the sum of all terms is 196, find the
common difference and number of terms.

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Answer: d = 4, n = 14

Explanation:

$S_n=(a_1+a_n)/(2)\cdot n$

$\text{Given:}\quad S_n=196, a_1=-12, a_n=40\\\\\\196=(-12+40)/(2)\cdot n\\\\392=28n\\\\14=n$

$a_(n)=a_1+d(n-1)\\a_(14)=a_1+d(14-1)\\40=-12+d(14-1)\\52 = 13d\\4=d$

White Island answered May 18, 2021

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