Find the sum of a finite geometric sequence from n = 1 to n = 7, using the expression −4(6)n − 1.

Answer 1

I suspect a notational problem.

Why the -4(6)n?
Is there supposed to be an exponent, as in 2^3=8?

Do you mean -4*6^(n-1) ?
That is, the terms are
-4,24,-144,...

Anyway, just plug your numbers into the formula for the sum of a geometric sequence.

Sn = a (1-r^n)/(1-r)