Question

Someone please help !!! find the sum of the first 45 terms in this geometric series -.5+1.5-4.5...

Answer 1

Explanation:

The given GP is : -0.5+1.5-4.5........

It is required to find the sum of 45 terms of GP.

From this GP, first term is (-0.5).

Common ratio is,
`r=(1.5)/(-0.5)=-3`

The formula use to find the sum of n terms of a GP is given by :

`S_n=(a(1-r^n))/(1-r),r<1`

Substituting all values in above formula :

`S_(45)=((-0.5)(1-(-3)^(45)))/(1-45)`

`S_(45)=(1)/(88)\cdot\left(1-\left(-3\right)^(45)\right)`

Hence, this is the required solution.