Find the missing term in the following number series:

15, 34, 57, 86, ?, 154

Question

Find the missing term in the following number series:

15, 34, 57, 86, ?, 154

Accepted Answer

**Solution:**

1. Observe the given series: 15, 34, 57, 86, ?, 154

2. Calculate the differences between consecutive terms:
   - 34 - 15 = 19
   - 57 - 34 = 23
   - 86 - 57 = 29

3. The differences are increasing but not by a fixed amount. Let's check the pattern of differences:
   - 19, 23, 29

4. These differences themselves are increasing by 4 and then 6, which is irregular. Let's check if these are prime numbers:
   - 19 (prime), 23 (prime), 29 (prime)

5. The next prime number after 29 is 31, then 37.

6. Add 31 to 86:
   $$86 + 31 = 117$$

7. Add 37 to 117:
   $$117 + 37 = 154$$

8. This matches the last term given in the series.

**Answer:** The missing term is $\boxed{117}$.

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