Let t 1 , t 2 ,… be real numbers such that t 1 + t 2 + … + t n = 2n 2 + 9n + 13, for every positive integer n ≥ 2. If t k = 103, then k equals

Question

Let t 1 , t 2 ,&hellip; be real numbers such that t 1 + t 2 + &hellip; + t n = 2n 2 + 9n + 13, for every positive integer n &ge; 2. If t k = 103, then k equals

Accepted Answer

24 — S k = 2k 2 + 9k + 13 S k-1 = 2(k-1) 2 + 9(k-1) + 13 &rArr; T k = S k - S k-1 = 2k 2 + 9k + 13 - [2(k-1) 2 + 9(k-1) + 13] &rArr; T k = S k - S k-1 = 4k + 7 If t k = 103 &rArr; 4k + 7 = 103 or k = 24. Hence, 24.

CAT 2018 Slot 2 — QA Question 30

Answer & solution