Verified answer

It is multiplied by 5 everytime

5^x = next # in the sequence (starting at x = 0)

5^0 + 5^1 + 5^2 + 5^3 + 5^4 + 5^5 + 5^6 = 19,531

the sum of the first n terms of a geometric series is:

S = (1 - r^n)/(1-r)

where a is the first term of the series (in this case a = 1) , and r is the common ratio (in this case r = 5), and we are asked to find for n = 7

So...

S = (1 - r^n)/(1-r)

S = (1 - 5^7)/(1-5)

S = (1 - 78,125) / (-4)

S = (-78,124) / (-4)

S = 19,531

S7 = (1 - (5)^7)/(1 - 5) = (5^7 - 1)/4 = 19,531

this is a geometric series where a₁=1 and r=5

Sn =a₁(qⁿ-1) / q-1

S7= 1*(5^7 -1)5-1 =>5^6/4 => 19531