What number will replace the question mark in the following series?

400, 274, 209, 181, 172, ?

Question

What number will replace the question mark in the following series?

400, 274, 209, 181, 172, ?

Accepted Answer

**Solution:**

1. Observe the pattern in the series: 400, 274, 209, 181, 172, ?

2. Calculate the differences between consecutive terms:
   - $400 - 274 = 126$
   - $274 - 209 = 65$
   - $209 - 181 = 28$
   - $181 - 172 = 9$

3. Notice these differences correspond to squares plus 1:
   - $126 = 11^2 + 1 = 121 + 5$ (Check carefully)

Let's verify the original pattern given:
   - $400 - (5^3 + 1) = 400 - (125 + 1) = 400 - 126 = 274$
   - $274 - (4^3 + 1) = 274 - (64 + 1) = 274 - 65 = 209$
   - $209 - (3^3 + 1) = 209 - (27 + 1) = 209 - 28 = 181$
   - $181 - (2^3 + 1) = 181 - (8 + 1) = 181 - 9 = 172$

4. Following this pattern, the next term is:
   - $172 - (1^3 + 1) = 172 - (1 + 1) = 172 - 2 = 170$

**Answer:** $170$

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