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

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Correct Answer: 24

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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CAT 2018 Quant Questions
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