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Ull infinite 1 G.P. with common ration, ...

Ull infinite 1 G.P. with common ration, Welt T = arr-+bn + C 3 Ans.(a) SOLUTION We have 1² – 2² + 3² – 4² = (1-2) (1 + 2) + =-(1+2+3+4 :) If the differences between consecutive terms of the se- quence T2 - T1, T3 - T2, T4 - Tz , ... are in (a) A.P., then In = anº + bn² + cn+d (b) G.P., then Tn = arn-1 + bn+ cn+d ILLUSTRATION 1 The sum of first 9 terms of the series 13 13 + 23 1² +2²+ 33 -+..., is 1' 1+3 1+3+5 (a) 142 (b) 192 (c) 71 (d) 96 Ans. (d) (JEE (Main) 2015] ILLUSTRATION 4 I 1² – 2² + 3² -2 + (a) "617,(6) (1 – x) Ans. (a)

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