In known sequence an, an = 2N-1 (n is odd) an = 3 ^ n (n is even), find the first n terms and Sn

In known sequence an, an = 2N-1 (n is odd) an = 3 ^ n (n is even), find the first n terms and Sn

An = 2N-1 (n is odd) an = 3 ^ n (n is even)
If n is even
Then Sn = [A1 + a3 + A5 +... + a (n-1)] + [A2 + A4 + A6 +... + an]
=[1+5+9+...+2n-3]+[9+9^2+9^3+..+9^(n/2)]
=[1+(2n-3)]*(n/4)+9(3^n-1)/(9-1)
=(n-1)n/2+9/8*(3^n-1)
When n is odd, N + 1 is even
Sn=S(n+1)-a(n+1)
=n(n+1)/2+9/8[3^(n+1)-1]-3^(n+1)
=n(n+1)/2+1/8*3^(n+1)-9/8
That is, when n is even, Sn = (n-1) n / 2 + 3 / 8 * 3 ^ (n + 1) - 9 / 8
When n is odd, Sn = n (n + 1) / 2 + 1 / 8 * 3 ^ (n + 1) - 9 / 8