What should come in place of the ‘?’ in the given series? 2 10 43 176 709 ?
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.
| Step | Working | Result |
| 1 | 2 × 4 + 2 | 10 |
| 2 | 10 × 4 + 3 | 43 |
| 3 | 43 × 4 + 4 | 176 |
| 4 | 176 × 4 + 5 | 709 |
| 5 | 709 × 4 + 6 | 2842 |
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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