Answer to Question #22348 in Discrete Mathematics for brett

Question

Find the Sum of the first 25 terms of the poulation sequence defined by Pn=37+11n

Answer 1

Notice that the numbers P0, P1, ... constitute arithmetic progression with initial term P0=37 and difference d=11.
Hence the sum of the first 25 terms
S = P0 + P1 + ... + P24 = 25*(P0+P24)/2 = 25*(37+37+11*24)/2 = 25*(37+11*12) = 4225.