Question

complete the series 10,37,82,145,226​

Answer 1

The next term is "325".

Step-by-step explanation:

The given sequence are:

10, 37, 82, 145, 226​

To find, the next term = ?

The pattern follow:

$3^{2} +1,6^{2} +1,9^{2} +1,12^{2} +1,15^{2} +1,....$

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

$37=6^{2} +1=36+1=37$

$82=9^{2} +1=81+1=82$

$145=12^{2} +1=144+1=145$

$226=15^{2} +1=225+1=226$

Similarly,

The next term =$18^{2} +1=324+1=325$

Hence, the next term is "325".

Answer 2

Given:

A series of numbers 10,37,82,145,226​.  

To Find:

The next term in the series is?  

Solution:

The given problem can be solved by developing a common logic between every term.  

1. The given series is 10,37,82,145,226​  

2. The first term in the series is obtained as,  

=> First term = 3² + 1 = 10,  

3. The second term in the series is obtained as,  

=> Second term = 6² + 1 = 37,  

4. The third term in the series is obtained as,  

=> Thirdd term = 9² + 1 = 82,  

5. The fourth term in the series is obtained as,  

=> Fourth term = 12² + 1 = 145,  

6. The Fifth term in the series is obtained as,  

=> Fifth term = 15² + 1 = 226,  

7. The sixth term of the series can be obtained using similar logic,

=> Sixth term = 18² + 1 = 325.

 

Therefore, the next number in the series is 325.