Find the missing term in the series given below: 10, 11, 13, 17, 25, 31, 33, ?

We can look at the difference:

11−10 = 1

13−11 = 2

17−13 = 4

25−17 = 8

31−25 = 6

33−31 = 2

Those differences follow the pattern of powers of 2 reduced modulo 10:

$$1(2⁰),2(2^1),4(2^2),8(2^3),16→6(2⁴mod10),32→2(2⁵mod10)$$

Next is 64 →4 (2⁶ mod 10)

So the next difference should be 4. Hence the next term = 33 + 4 = 37.

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