Find the missing number in the series:

24, 49, ?, 219, 388, 677

Question

Find the missing number in the series:

24, 49, ?, 219, 388, 677

Accepted Answer

**Solution:**

1. Observe the pattern between consecutive terms:

- From 24 to 49:
     $$24 + 5^2 = 24 + 25 = 49$$

2. To find the missing term (let it be *x*), add the next square number:

- $$x = 49 + 7^2 = 49 + 49 = 98$$

3. Check if this fits the next terms:

- Next term after *x*:
     $$98 + 11^2 = 98 + 121 = 219$$

- Next:
     $$219 + 13^2 = 219 + 169 = 388$$

- Next:
     $$388 + 17^2 = 388 + 289 = 677$$

4. The pattern of adding consecutive odd squares (5², 7², 11², 13², 17²) fits except the missing term calculated as 98.

**Answer:** 98

**Note:** The original answer given was 108, but based on the pattern of adding squares of odd numbers, the missing term should be 98.

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