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Question

What should come in place of the ‘?’ in the given series?

2 10 43 176 709 ?

The correct answer is

2842

Compare each term with the one before it. Multiplying by 4 brings each term close to the next, and the remainder grows by 1 each time.

StepWorkingResult
12 × 4 + 210
210 × 4 + 343
343 × 4 + 4176
4176 × 4 + 5709
5709 × 4 + 62842

So each term is obtained as (previous term × 4) + k, with k = 2, 3, 4, 5, 6. The missing term is 709 × 4 + 6 = 2836 + 6 = 2842.

Check: 2842 – 6 = 2836 and 2836 ÷ 4 = 709, so the rule works backwards from the missing term to the last given term.

Hence, 2842.

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