Question

Write an expression that gives the requested sum.

The sum of the first 20 terms of the geometric sequence with first term 6 and common ratio 3
s20 =

Answer 1

The expression to give the requested sum after simplifying,
`S_(20)` =
`{3(3^(20)-1) }`

Explanation:

To find the sum of first 20 terms,

a = 6, r = 3

By formula,
`S_(n) = (a(r^(n)-1) )/(r-1)`

substitute the values in the above formula, the equation becomes,

`S_(20) = (6(3^(20)-1) )/(3-1)`

`S_(20) = (6(3^(20)-1) )/(2)`

`S_(20)` =
`{3(3^(20)-1) }`