CAT 2018 Progression Question (Medium)

Question

Let be real numbers such that , for every positive integer . If , then equals TITA .

Accepted Answer

Step 1 We are given the sum of the first n terms S n t t ... t 2n 9n 13, for n 2 To find t , use t S k S k 1 Step 2 Use the formula S k 2k 9k 13 S k 1 2 k 1 9 k 1 13 2 k 2k 1 9 k 1 13 2k 4k 2 9k 9 13 2k 5k 6 Now subtract t S k S k 1 2k 9k 13 2k 5k 6 4k 7 Step 3 We are given t 103 4k 7 103 4k 96 k 24

CAT 2018

Quantitative

Progression

Medium

Let $t_1, t_2, \dots$ be real numbers such that $t_1 + t_2 + \dots + t_n = 2n^2 + 9n + 13$ , for every positive integer $n \geq 2$ . If $t_k = 103$ , then $k$ equals (TITA).

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