a-0-2-a-n-a-n-1-2n-a-n-

Question Number 161930 by Rasheed.Sindhi last updated on 24/Dec/21

{\begin{cases} a_{0} = - 2 \\ a_{n} = a_{n - 1} + 2 n \end{cases}; a_{n} = ?

Answered by mr W last updated on 24/Dec/21

a_{n} = a_{n - 1} + 2 \times n

a_{n - 1} = a_{n - 2} + 2 \times (n - 1)

\dots

a_{2} = a_{1} + 2 \times 2

a_{1} = a_{0} + 2 \times 1

Σ a l l :

a_{n} = a_{0} + 2 (1 + 2 + \dots + n) = a_{0} + n (n + 1)

w i t h a_{0} = - 2

a_{n} = - 2 + n (n + 1) = n^{2} + n - 2

Commented by Rasheed.Sindhi last updated on 24/Dec/21

T h a n X S i r!