Given below are two number series. Series I is incomplete, and Series II contains one incorrect number but follows the pattern of Series I.

Series I: 11, P, 181, 350, 639, 1000

Series II: 242, 251, 255, 280, 329, 450, 619

If 'y' is the incorrect number in Series II, find the value of $2y + 1$.

Question

Given below are two number series. Series I is incomplete, and Series II contains one incorrect number but follows the pattern of Series I.

Series I: 11, P, 181, 350, 639, 1000

Series II: 242, 251, 255, 280, 329, 450, 619

If 'y' is the incorrect number in Series II, find the value of $2y + 1$.

Accepted Answer

**Solution:**

1. Analyze the pattern in Series II:
   - Starting from 242, the differences between consecutive terms are squares of prime numbers.

2. Calculate the differences:
   - $242 + 2^2 = 242 + 4 = 246$
   - $246 + 3^2 = 246 + 9 = 255$
   - $255 + 5^2 = 255 + 25 = 280$
   - $280 + 7^2 = 280 + 49 = 329$
   - $329 + 11^2 = 329 + 121 = 450$
   - $450 + 13^2 = 450 + 169 = 619$

3. Compare these with the given Series II:
   - The second term is given as 251, but according to the pattern, it should be 246.
   - Therefore, the incorrect number $y$ is 251.

4. Find the required value:
   $$2y + 1 = 2 	imes 251 + 1 = 502 + 1 = 503$$

**Answer:** 503

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