Find the missing term in the series:

68, ?, 407, 470, 496, 503

Question

Find the missing term in the series:

68, ?, 407, 470, 496, 503

Accepted Answer

**Solution:**

1. Observe the given series: 68, ?, 407, 470, 496, 503.

2. Calculate the differences between the known consecutive terms:
   - Between 407 and 470: $470 - 407 = 63$
   - Between 470 and 496: $496 - 470 = 26$
   - Between 496 and 503: $503 - 496 = 7$

3. The differences are decreasing: 63, 26, 7.

4. Now, find the difference between the missing term and 407:
   - Let the missing term be $x$.
   - The difference between $x$ and 407 should be greater than 63 (since the differences are decreasing).

5. Check the difference between 68 and $x$:
   - If $x = 283$, then $283 - 68 = 215$
   - Then, $407 - 283 = 124$
   - Then, $470 - 407 = 63$
   - Then, $496 - 470 = 26$
   - Then, $503 - 496 = 7$

6. The differences are: 215, 124, 63, 26, 7, which are decreasing consistently.

7. Hence, the missing term is **283**.

**Answer:** 283

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