Question

Evaluate the geometric series. Round to the nearest hundredth.
Please help me!!!

Answer 1

32.59

Explanation:

The n th term of a geometric sequence is

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio )

4
`((8)/(9)) ^(n-1)` ← is the n th term expression

with a = 4 and r =
`(8)/(9)`

The sum of n terms of a geometric sequence is

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

`S_(20)` =
`(4((1-(8)/(9)) ^(20)) )/(1-(8)/(9) )`

=
`(4(1-(8^(20) )/(9^(20) ) ))/((1)/(9) )`

= 36( 1 - 0.0948)

= 36(0.905)

= 32.59 ( to the nearest hundredth )

Answer 2

32.59

That's what my calculator said

also I use acellus too Hi friend!