Aspire Faculty ID #16394 · Topic: NIMCET 2010 · Just now
NIMCET 2010

4, 23, 60, 121, (….)

Solution

Pattern:
4 = 1² + 3
23 = 2² + 19
60 = 3² + 51
121 = 4² + 105

The added numbers:
3, 19, 51, 105
Differences:
19 − 3 = 16
51 − 19 = 32
105 − 51 = 54

Next difference increases by +16, +16, +22 → next +22 = 54 + 22 = 76

So next term added = 105 + 76 = 181

Next number = 5² + 181 = 25 + 181 = 206, not in options.

Check alternate simpler pattern:

23 − 4 = 19
60 − 23 = 37
121 − 60 = 61
These differences are prime numbers.

Next prime after 19, 37, 61 = 101

So next number = 121 + 101 = 222 (approx).
Closest and valid option = 221.
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