What number would replace question mark (?) in the series given below? 3, 8,…
2023
What number would replace question mark (?) in the series given below?
3, 8, 17, 32, 57, ?, 177
Answer: A. 100 — CONCEPTFor a sequence whose consecutive differences are not constant, inspect the differences for a second-level rule. If each new difference is generated…
- A.
100
- B.
89
- C.
95
- D.
106
Attempted by 2 students.
Show answer & explanation
Correct answer: A
CONCEPT
For a sequence whose consecutive differences are not constant, inspect the differences for a second-level rule. If each new difference is generated from the preceding difference, apply that rule before adding the difference to the preceding term.
APPLICATION
The first differences are 5, 9, 15 and 25.
These follow 9 = 2 × 5 − 1, 15 = 2 × 9 − 3, and 25 = 2 × 15 − 5; the subtracted numbers are consecutive odd numbers.
The next difference is 2 × 25 − 7 = 43.
Therefore, the missing term is 57 + 43 = 100.
CROSS-CHECK
The following difference is 2 × 43 − 9 = 77, and 100 + 77 = 177, which reproduces the final given term. Hence, the missing number is 100.