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).