Question

Find the next number in the series. 10, 74, 202, 394....​

Answer 1

Answer:

650

Step-by-step explanation:

10 => first 2 odd numbers square sum => 1²+3² = 10

74 => next 2 odd numbers square sum => 5²+7² = 74

for 202 => 9²+11²

     394=> 13²+15²

     hence next number is 17²+19² = 650.

Answer 2

Given:

10, 74, 202, 394....​

Solution:

To find the next term of the series, first observe the pattern and find out the change that occurs on moving from one to to another,

$\[\begin{array}{l}10 + 64 = 74\\74 + \left( {64 + 64} \right) = 202\\202 + \left( {64 + 64 + 64 = 394} \right)\\394 + \left( {64 + 64 + 64 + 64} \right) = 650\end{array}\]$

Hence, the next number in the series is 650.