P_k - P_(k-1) = 2*3^k
Sum both sides from k = 2 to k = n. Left hand side becomes:
P_2 - P_1 + P_3 - P_2 + P_4 - P_3 + P_5 - P_4 + .....+ P_n - P_(n-1) =
P_n - P_1
Right hand side is:
2* [3^2-3^(n+1)]/(1-3) =3^(n+1) - 9
P_n - P_1 = 3^(n+1) - 9 --->
P_n = 3^(n+1) -7
Use iteration to guess an explicit formula for the sequence.
Pk=Pk-1+2*3^k
P1=2
1 answer
1 answer