Step-by-step 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, [tex]r=\dfrac{1.5}{-0.5}=-3[/tex]
The formula use to find the sum of n terms of a GP is given by :
[tex]S_n=\dfrac{a(1-r^n)}{1-r},r<1[/tex]
Substituting all values in above formula :
[tex]S_{45}=\dfrac{(-0.5)(1-(-3)^{45})}{1-45}[/tex]
[tex]S_{45}=\dfrac{1}{88}\cdot\left(1-\left(-3\right)^{45}\right)[/tex]
Hence, this is the required solution.
