Given the string (an),n>=1 and the sum a1+a2+a3+...+an=(5n^2+6n), what are an and a1?

If the sum a1 + ... + an = 5n^2+6n, then the
sum:

a1 + ... + a(n-1) = 5(n-1)^2 +
6(n-1)

We'll determine an:

a1
+ ... + an - a1 - ... - a(n-1) = 5n^2 + 6n - 5(n-1)^2 -
6(n-1)

We'll eliminate like terms and we'll
get:

an = 5n^2 + 6n - 5(n-1)^2 -
6(n-1)

We'll raise to square and we'll combine like terms
from the right side:

an = 5n^2 + 6n - 5n^2 + 10n - 5 - 6n +
6

an = 10n + 1

We can
determine any other term of the string, replacing n by any natural
value.

For n=1 => a1 =
10+1

a1 = 11

The
requested terms are: a1 = 11 and an = 10n + 1.