In a big, red box, there are 7 smaller blue boxes. In each of the blue boxes, there are 7 black boxes. In each of the black boxes, there are 7 yellow boxes. In each of those yellow boxes, there are 7 tiny, gold boxes. How many boxes are there altogether? Explain your answer.
Number of red = 1
number of blue = 7
number of blacks = 7*7 = 7^2
number of yellows = 7^3
number of golds = 7^4
you want the sum of this geometric series, that is
7 + 7^2 + 7^3 + 7^4
the series has a = 7, r = 7, and n = 4
sum(4) = 7(7^4 - 1)/(7-1)
= 7*2400/6 = 2800