Mathematical Reasoning MCQ - Number Series

26 Find the wrong number in the sequence.
125, 127, 130, 135, 142, 153, 165

Prime number (numbers that are divisible by 1 and themselves only) starting with 2 are being added to each number to get the subsequent numbers.
Thus, the sequence of numbers can be read as 125, 125 + 2, 127 + 3, 130 + 5, 135 + 7, 142 + 11, and 153 + 13.
Hence, the last number should be 166.

27 Find the missing number in the following series.
3, 10, 101,?

Each term in the series is obtained by adding 1 to the square of the preceding term.
Hence, the missing term = (101)² + 1 = 10,202.

28 Find the missing number in the following series.
1, 1, 4, 8, 9, 27, 16, ?

It is a question of mixed series.
(i) Numbers at 1st, 3rd, 5th, and 7th places are squares of 1, 2, 3 and 4.
(ii) Numbers at 2nd, 4th, 6th, and 8th places are cubes of 1, 2, 3, 4 and 5. Hence, the answer is 4³ = 64.

29 Find the missing number in the following series.
3, 5, 13, 43, 177, ?

The pattern is
3 × 1 + 2 = 5
5 × 2 + 3 = 13
13 × 3 + 4 = 43
43 × 4 + 5 = 177
177 × 5 + 6 = 891
Hence, (a) is the answer.

30 Find the missing number in the following series.
3, 4, 7, 7, 13, 13, 21, 22, 31, 34, ?

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, ...
Hence, the missing term = 31 + 12 = 43.