# CAT 2018 Quant Questions

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

It is given that ${t_1} + {t_2} + ... + {t_n} = 2{n^2} + 9n + 13$, for every positive integer .

We can say that ${t_1} + {t_2} + ... + {t_k} = 2{k^2} + 9k + 13$ ... (1)

Replacing k by (k-1) we can say that

${t_1} + {t_2} + ... + {t_{k - 1}} = 2{(k - 1)^2} + 9(k - 1) + 13$ ... (2)

On subtracting equation (2) from equation (1)

$\Rightarrow$ ${t_k} = 2{k^2} + 9k + 13 - 2{(k - 1)^2} + 9(k - 1) + 13$

$\Rightarrow$ $103 = 4k + 7$

$\Rightarrow$ $k = 24$

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