1, 9, 25, 49, 81,?

The pattern is + 5, - 2, + 5, - 2,.....

So, missing term = 36 - 2 = 34.

Clearly, 3 + 6 = 9, 9 + 6 = 15,.....

So, the series is an A.P. in which a = 3 and d = 6.

Therefore 21st term = a + (21 - 1) d = a + 20d = 3 + 20 x 6 = 123.

Each term in the series is the product of the digits of the preceding term.

So, missing term = 1 x 8 = 8.

The pattern is + 3, + 6, + 12, + 24,.....

So, missing term = 46 + 48 = 94.

The terms of the given series are numbers formed by joining together consecutive

odd numbers in order i.e. 1 and 3, 3 and 5, 5 and 7, 7 and 9, 9 and 11, .....

So, missing term = number formed by joining 11 and 13 = 1113.

The given series consists of squares of consecutive odd numbers

i.e. 1², 3², 5², 7²,.....

So, missing term = 9² = 81.

The pattern is + 0, + 3, + 8, + 15, ..... i.e. + (l² - 1), + (2² - 1), + (3² - 1), + (4² - 1), .....

So, missing term = 28 + (5² - 1) = 28 + 24 = 52.

The pattern is + 2, + 6, + 6, + 10, + 10,.....

So, missing term = 14 + 10 = 24.

The pattern is + 4, + 9, + 16, + 25, + 36, ..... i.e. + 2², + 3², + 4², + 5², + 6²,.....

So, missing term = 91 + 7² = 91 + 49 = 140.

The given series consists of numbers each of which, on dividing by 7, leaves a

remainder 3. No other number except 346 satisfies the property.