How many terms of the AP 3, 7, 11, 15,…. Will make the sum 406?A. 10 – InterviewSolution

InterviewSolution

1.	How many terms of the AP 3, 7, 11, 15,…. Will make the sum 406?A. 10B. 12C. 14D. 20
Answer» Correct Answer - C Let `S_(n) = 406. "Then," (n)/(2)[2 xx 3 + (n-1) xx 4] = 406` `rArr (n)/(2)(6+4n-4) = 406 rArr (n)/(2)(4n +2) = 406` `rArr n(2n+1) = 406 rArr 2n^(2) + n - 406 = 0` `therefore n = (-1+-sqrt(1+3248))/(4) = (-1+sqrt(3249))/(4)` [neglecting negative value] `rArr n = (-1+57)/(4) = (56)/(4) = 14`

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