Chapter test: Number Series

Explanation: The pattern is n cubed minus 1 for n = 1 to 6, so the answer is 216 − 1 = 215. Shortcut: each term sits just below a cube, since 7 is near 8 and 26 near 27. Forgetting the minus one gives 216.

Explanation: The differences are 3, 6, 9 and 12, all multiples of 3, so the next difference is 15 and the answer is 35 + 15 = 50. Repeating the previous difference of 12 gives 47, which is the trap.

Explanation: The primes below 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47, which is 15. Counting 1 as prime gives 16 and dropping 2 gives 14. The figure 25 is the count of primes below 100.

Explanation: Each term is the sum of the previous three terms, since 4 + 7 + 13 = 24, so the next is 7 + 13 + 24 = 44. Adding only the previous two gives 13 + 24 = 37, the classic Fibonacci trap.

Explanation: Each term is the previous one multiplied by 2 plus 1, so 63 x 2 + 1 = 127. Shortcut: every term is one less than a power of 2, being 4 − 1, 8 − 1, 16 − 1, 32 − 1 and 64 − 1, so the next is 128 − 1. Only doubling gives 126.

Explanation: This is an alternate series. Odd positions run 4, 8, 12, 16 rising by 4, and even positions run 30, 26, 22 falling by 4. The blank is the eighth term, an even position, so the answer is 22 − 4 = 18. The value 20 continues the odd-position series instead.

Explanation: The pattern is x n + n with n rising: 1 x 1 + 1 = 2, 2 x 2 + 2 = 6, 6 x 3 + 3 = 21, 21 x 4 + 4 = 88, so the next is 88 x 5 + 5 = 445. Forgetting to add the 5 gives 440.

Explanation: The common difference is +5, so the next term is 22 + 5 = 27. Using nth term = a + (n − 1) x d, the fifth term is 7 + 4 x 5 = 27. The values 26 and 28 are plus or minus one distractors.

Explanation: The rule is n x (n + 1), giving 2, 6, 12, 20, 30, 42, 56, so the sixth term should be 42 and not 44. The differences 4, 6, 8, 10, 14, 12 confirm it, because the two abnormal values sit on either side of 44. The term 56 is correct as 7 x 8.

Explanation: These are the squares of consecutive primes 2, 3, 5, 7 and 11, so the next is 13 squared = 169. The series skips 16 and 36 because 4 and 6 are not prime, which rules out 144, 196 and 225 as squares of 12, 14 and 15.