Question

Use the formula to evaluate the series -3 + 6 - 12 +24 - ...-az.

Answer 1

Your sum =
`(-2)^(z)` - 1

S = ( (-2)^n - 1), If you let n = z, then S = (-2)^z - 1

Explanation:

I can use a formula to find the sum of the first n terms.

we have -3, 6, -12, 24, ... etc.

common ratio = r = -2

first term = -3

a_1 = -3

Then: a_n = a_1 * r ^(n -1)

a_n = (-3) * (-2)^(n - 1) is the general formula for the nth term

Sum of first n terms = S = a_1 * (r^n - 1) / (r - 1)

so...

S = (-3) * ((-2)^n - 1 )/ (-2 - 1)

which simplifies to

S = (-3) *((-2)^n - 1) / (-3)

S = ( (-2)^n - 1)

If you let n = z, then S = (-2)^z - 1