Question

Question #f32bc

Answer 1

See explanation.

Explanation:

If we write some terms of the sequence we get:

`a_0=0`

`a_1=0+1=1`

`a_2=1+2=3`

`a_3=3+3=6`

From the given example we see that the `n`-th term of the sequence is the sum of `n` natural numbers:

`a_n=1+2+3+...+n`

To find the formula for the term we can treat it as the sum of `n` terms of arithmetic sequence with `a_1=1` and `d=1`

Using the formula for the sum of arithmetic sequence we get:

`a_n=((1+n)*n)/2`

After simplifying we get:

`a_n=(n^2+n)/2`