Use iteration to guess an explicit formula for the sequence.

Pk=Pk-1+2*3^k
P1=2

1 answer

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
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