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Question

What should come in place of the question mark (?) in the given series?

90 106 74 122 ? 138

The correct answer is

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.

Term901067412258138
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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