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
Explanation:
Sk = 2k2 + 9k + 13
Sk-1 = 2(k-1)2 + 9(k-1) + 13
⇒ Tk = Sk - Sk-1 = 2k2 + 9k + 13 - [2(k-1)2 + 9(k-1) + 13]
⇒ Tk = Sk - Sk-1 = 4k + 7
If tk = 103
⇒ 4k + 7 = 103 or k = 24.
Hence, 24.
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