The given sequence is a combination of two series : I. 3, 7, 13, 21, 31, ? and II. 4, 7, 13, 22, 34 The pattern in I is + 4, + 6, + 8, + 10,..... The pattern in II is + 3, + 6, + 9, + 12,..... So, missing term = 31 + 12 = 43.
Clearly, 5 x 2 = 10, 10 x 2 = 20, 20 x 2 = 40,..... So, the series is a G.P. in which a = 5 and r = 2. Let 1280 be the rath term of the series. Then, 5x2n-1 = 1280 ⇔ 2n-1 = 256 = 28 ⇔ n - 1 = 8 ⇔ n = 9.
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