Question

How do you find `S_n` for the geometric series `a_1=625`, r=3/5, n=5?

Answer 1

`"see explanation"`

Explanation:

`"For a geometric series the sum to n terms is"`

`•color(white)(x)S_n=(a_1(1-r^n))/(1-r)color(white)(x)r!=1`

`"here "a_1=625" and "r=3/5`

`rArrS_n=(625(1-(3/5)^n))/(1-3/5)`

`color(white)(S_n)=3125/2(1-(3/5)^n)`

`"for "n=5`

`S_5=3125/2(1-(3/5)^5)`

`color(white)(S_5)=3125/2(1-243/3125)`

`color(white)(S_5)=3125/2xx2882/3125=1441`