Number Series MCQs with Answers & Explanations

The differences between consecutive terms are consecutive odd numbers: +3, +5, +7, +9. The next difference is +11, giving 27 + 11 = 38.

The series follows the pattern n^2 + 1 for n = 1, 2, 3, 4, 5. For n = 6, 6^2 + 1 = 37.

The sequence consists of consecutive cubes: 1^3, 2^3, 3^3, 4^3, 5^3. The next term is 6^3 = 216.

The terms follow the formula n^3 + n^2: 1^3 + 1^2 = 2, 2^3 + 2^2 = 12, 3^3 + 3^2 = 36, 4^3 + 4^2 = 80, 5^3 + 5^2 = 150. For n = 6, 6^3 + 6^2 = 216 + 36 = 252.

Each term is obtained by multiplying the previous number by 2: 80 \times 2 = 160.

The multiplier increases by 1 at each step: \times 2, \times 3, \times 4, \times 5. The next operation is 840 \times 6 = 5040.

The numbers subtracted are consecutive squares: -2^2 (-4), -3^2 (-9), -4^2 (-16), -5^2 (-25). The next subtraction is -6^2 (-36), so 46 - 36 = 10.

This is the Fibonacci sequence, where each term is the sum of the two preceding terms: 8 + 13 = 21.

The sequence consists of consecutive prime numbers. The prime number immediately following 13 is 17.

The difference between consecutive numbers increases by 5 each time: +5, +10, +15, +20. Adding 25 to 56 gives 81.

Each term is generated by multiplying by 2 and subtracting 2: (130 \times 2) - 2 = 260 - 2 = 258.

Each term is obtained by multiplying the previous term by 3 and adding 1: (121 \times 3) + 1 = 363 + 1 = 364.

The terms are cubes of consecutive prime numbers: 2^3, 3^3, 5^3, 7^3, 11^3. The next prime is 13, and 13^3 = 2197.

The sequence follows n^3 - n: 1^3 - 1 = 0, 2^3 - 2 = 6, 3^3 - 3 = 24, 4^3 - 4 = 60, 5^3 - 5 = 120, 6^3 - 6 = 210. For n = 7, 7^3 - 7 = 343 - 7 = 336.

The sequence follows the pattern n^3 - n^2 starting at n = 2: 2^3 - 2^2 = 4, 3^3 - 3^2 = 18, 4^3 - 4^2 = 48, 5^3 - 5^2 = 100, 6^3 - 6^2 = 180. For n = 7, 7^3 - 7^2 = 343 - 49 = 294.

The sequence alternates between powers of 2 (2^1, 2^2, 2^4 or powers of 4) and powers of 3: 2, 4, 16 at odd positions (2^1, 2^2, 2^4 \rightarrow powers doubled: 2^1=2, 2^2=4, 4^2=16, 16^2 or doubling exponents 2^1, 2^2, 2^4, 2^6=64) and 3^1=3, 3^2=9, 3^3=27 at even positions. Thus, the next term is 2^6 = 64 (or 4^3 = 64).

The differences between consecutive terms are consecutive prime numbers: +2, +3, +5, +7. The next prime to add is 9 is not prime, so +11: 29 + 11 = 38.

Consecutive even numbers are subtracted: -6, -8, -10, -12. The next difference is -14, so 54 - 14 = 40.

The sequence represents factorials of natural numbers: 1!, 2!, 3!, 4!, 5!, 6!. The next term is 7! = 5040.

The pattern is (5 \times 1) + 1 = 6, (6 \times 2) + 2 = 14, (14 \times 3) + 3 = 45, (45 \times 4) + 4 = 184. The next term is (184 \times 5) + 5 = 920 + 5 = 925.