Question

Help me please!!!!!!!!

Answer 1

The sum is approximately 42.56

Explanation:

Notice that you are dealing with a series whose first term is :

`3 \, ((3)/(2))^0 = 3\,*\,1=3`

followed by sum of terms of the form:

`a_1=3\,((3)/(2) )^1\\a_2=3\,((3)/(2) )^2\\a_3=3\,((3)/(2) )^3\\a_4=3\,((3)/(2) )^4\\a_5=3\,((3)/(2) )^5`

and this is a geometric sequence of common ratio given by:
`(3)/(2)` (the value you need to multiply one term of the geometric sequence in order to find the following one)

Then, we can use the general formula for a partial sum of a geometric sequence for these last 5 terms for which m=5, the common ratio r =
`(3)/(2)` , and
`a` = 3:

`S_m=a(r^m-1)/(r-1)\\S_5=3 (((3)/(2))^5 -1)/((3)/(2)-1)\\S_5=39.5625`

So, the total sum of the six terms is:

Total sum = 3 +39.5625 = 42.5625

which can be rounded to hundredth: 42.56