Question

What is the value of S4 for HURRY PLEASE !!!

Answer 1

5
`(1)/(4)`

Explanation:

The sum to n terms of a geometric sequence is

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

where a is the first term and r the common ratio

The expression inside the summation is

4
`((1)/(4)) ^(n-1)` ← the nth term of a geometric sequence

with a = 4 and r =
`(1)/(4)` , then

`S_(4)` =
`(4(1-((1)/(4)) ^(3)) )/(1-(1)/(4) )`

=
`(4(1-(1)/(64)) )/((3)/(4) )`

=
`(16)/(3)` (
`(63)/(64)` )

=
`(21)/(4)`

= 5
`(1)/(4)`