any natural number.
I. 1st, 4th, 7th, 10th, 13th terms i.e. 2, 4, 6, 8, ?
II. 2nd, 5th, 8th, 11th terms i.e. 1, 4, 7, 10
III. 3rd, 6th, 9th, 12th terms i.e. 2, 5, 8, 11
Clearly, I consists of consecutive even numbers. So, the missing term is 10.
So, missing term = 1127 + 8 = 1135.
So, missing term = 13 x 3 = 39.
So, missing term = 9 + 5 = 14.
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.
I. 13, 24, 35, 46, 57 and II. 32, 43, ?, 65, 76
The pattern in both I and II is + 11. So, missing term = 43 + 11 = 54.
So, missing term = 28 + 8 = 36.
So, missing term = (62 - 1) - (36 - 1) = 35.
So, missing term = 3 x 50 = 150.
So, missing term = 192 ÷ 2 = 96.
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