What should come in place of the question mark (?) in the given series? 90 106 74 122 ? 138
58
Find the differences between consecutive terms: 106 – 90 = +16, 74 – 106 = –32 and 122 – 74 = +48. The differences are multiples of 16 (16, 32, 48, …) with alternating signs.
So the next differences are –64 and +80. The missing term is 122 – 64 = 58, and the term after it is 58 + 80 = 138.
| Term | 90 | 106 | 74 | 122 | 58 | 138 |
| Difference | – | +16 | –32 | +48 | –64 | +80 |
Check: with 58 in place of the question mark, the last given term 138 is reproduced exactly as 58 + 80, so the rule fits the whole series.
Hence, 58.
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2, 5, 11, 23, 44, 77, ?
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