Question

What is the next number in this series 5,10,26,50,122 _____
please give reason also​

Answer 1

Answer:

Next number = 170

Step-by-step explanation:

Given,

5, 10, 26, 50, 122

5 = 2² + 1

10 = 3² + 1

26 = 5² + 1

50 = 7² + 1

122 = 11² + 1

Thus, the series follows as,

n² + 1, where n is any number.

Seing this,

2, 3, 5, 7, 11

All are prime.

So, the next prime after 11 is 13.

Therefore, next number will be

13² + 1 = 169 + 1

= 170

Answer 2

The next number in the series is 170.

Given: A series 5, 10, 26, 50, 122, __

To find: The next number in the series

Solution:

On carefully observing the given series, we find the following pattern:

The numbers in the given series are the squares of prime numbers starting from 2 plus 1.

i.e.,

5 = $2^{2}$ + 1 (4 + 1 = 5)

10 = $3^{2}$ + 1 (9 +1 = 10)

26 = $5^{2}$ + 1 (25 + 1 = 26)

50 = $7^{2}$ + 1 (49 + 1 = 50)

122 = $11^{2}$ + 1 (121 + 1 = 122)

Following the same pattern, the next prime number is 13. So, the next number in the series will be:

$13^{2}$ + 1 = 169 + 1 = 170

Hence, the required number is 170.

Project code - #SPJ3