Question

13, 74, 290, 650,.......

• A. $1248$
• B. $1370$
• C. $1346$
• D. $1452$
• E. $1625$

Answer 1

The correct option is A $1248$

Here we observe the first term 13 can be written as: $2^2+3^2$

Similarly other numbers can be written as:

$74:5^2+7^2$

$290:{11}^2+{13}^2$

$650:{17}^2+{19}^2$

Here, we observe that all above term of series can be written as sum of squares of two prime numbers which comes next to it's previous pair.

Like: $(2,3);(5,7);(11,13);(17,19)$ So, other pair of prime number will be $(23,29).$

Hence next term of given series will be:

$\Rightarrow {23}^2+{29}^2=1370$

So, correct answer is $1370$.