Question

Let t1, t2,… be real numbers such that t1+t2+…+tn = 2n2 +9n+13, for every positive integer n ≥ 2. If tk=103, then k equals

Answer 1

t1+t2+....+tn = 2n2+9n+13 -> (1)
t1+t2+....+tn-1 = 2(n-1)2+9(n-1)+13 -> (2)
From (2) (1), we get tn=(2n2+9n+13)-(2(n-1)2+9(n-1)+13) = 4n+7
Given tk = 103 ⇒ 4k+7 = 103 ⇒ k = 24