Problema Solution

Suppose you receive $x in January. Each month thereafter, you receive $50 dollars more than you received the month before. Write a factored polynomial that describes the total amount you receive January through May.

Answer provided by our tutors

let f(n) we the amount of money received as a salary for the n th month


January: f(1)= x + (1-1)*0

February: f(2) = x + 50

March: f(3) = x + 50 + 50 = x + 2*50

April: f(4) = x + 2*50 + 50 = x + 3*50

...........

f(n+1) = f(n) + 50

f(n + 1) = x + n*50


the total amount of money received from January through May (including the salary for May) is:


f(1) + f(2) + f(3) + f(4) + f(5) = x + x + 50 + x + 2*50 + x + 3*50 + x + 4*50 =


= 5*x + 50(1 + 2 + 3 + 4) = 5x + 500 = 5(x + 100).