Given two number series:

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

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

If 2 is added successively to the nearest prime number to *P* to form a new series, what is the 5th term of this new series?

Question

Given two number series:

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

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

If 2 is added successively to the nearest prime number to *P* to form a new series, what is the 5th term of this new series?

Accepted Answer

**Solution:**

1. First, identify the missing term *P* in Series I by examining the pattern:

- Starting from 11, add squares of prime numbers in increasing order:
     - $11 + 7^2 = 11 + 49 = 60$ which is *P*
     - $60 + 11^2 = 60 + 121 = 181$
     - $181 + 13^2 = 181 + 169 = 350$
     - $350 + 17^2 = 350 + 289 = 639$
     - $639 + 19^2 = 639 + 361 = 1000$

2. The nearest prime number to *P = 60* is either 59 or 61.

3. A new series is formed by starting from this nearest prime and adding 2 successively for each term.

4. Calculate the 5th term of this new series:

- Starting from 59:
     - 1st term: 59
     - 2nd term: 59 + 2 = 61
     - 3rd term: 61 + 2 = 63
     - 4th term: 63 + 2 = 65
     - 5th term: 65 + 2 = 67

- Starting from 61:
     - 1st term: 61
     - 2nd term: 61 + 2 = 63
     - 3rd term: 63 + 2 = 65
     - 4th term: 65 + 2 = 67
     - 5th term: 67 + 2 = 69

5. Therefore, the 5th term of the new series can be either 67 or 69.

**Answer:** (a) either 67 or 69

Answer

Answer