An algebra problem by sarvesh dubey

2^3 + 2 = 10

3^3 + 3 = 30

4^3 + 4 = 68

5^3 + 5 = 130

So , next term is ,

6^3 + 6 = 222 :)

There's this method of solving such sums, which doesn't work every time, but sometimes it does. You find the difference between consecutive terms repeatedly till the pattern is clearly visible.

$10,30,68,130$

$\Rightarrow 20, 38, 62$

$\Rightarrow 18, 24$

Here the pattern, multiples of six, is clearly visible, and we can predict the next number to be $30$ .

Hence the answer, $30+62+130=\boxed{222}$

The terms of the given sequence are obtained from n+(n^3).when n =6 we get 222

The diferrences between the number are, consecutively:

$20, 38, 62...$

We note that the differences increases $18$ then $24$ , in other words, they are multiples of $6$ . So, the next difference will be $30$ times more.

Then, we have that:

$130 + 62 + 30 = \boxed {222}$