Question

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

Answer 1

Answer:

Your sum = $(-2)^{z}$  -  1  

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

Step-by-step 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