Question

Write the next term of each of the following sequences :
$1,5,14,30,55,.....$

Answer 1

The series is as follows:-

$1^2=1$ (1st term)

$1^2+2^2=5$ (2nd term)

$1^2+2^2+3^2=14$

$1^2+2^2+3^2+4^2=30$

$1^2+2^2+3^2+4^2+5^2=55$

$1^2+2^2+3^2+4^2+5^2+6^2=91$......so on.

Hence, the next term in the series is 91.