Answer:
The sum is approximately 42.56
Step-by-step explanation:
Notice that you are dealing with a series whose first term is :
[tex]3 \, (\frac{3}{2})^0 = 3\,*\,1=3[/tex]
followed by sum of terms of the form:
[tex]a_1=3\,(\frac{3}{2} )^1\\a_2=3\,(\frac{3}{2} )^2\\a_3=3\,(\frac{3}{2} )^3\\a_4=3\,(\frac{3}{2} )^4\\a_5=3\,(\frac{3}{2} )^5[/tex]
and this is a geometric sequence of common ratio given by: [tex]\frac{3}{2}[/tex] (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 = [tex]\frac{3}{2}[/tex] , and [tex]a[/tex] = 3:
[tex]S_m=a(r^m-1)/(r-1)\\S_5=3 ((\frac{3}{2})^5 -1)/(\frac{3}{2}-1)\\S_5=39.5625[/tex]
So, the total sum of the six terms is:
Total sum = 3 +39.5625 = 42.5625
which can be rounded to hundredth: 42.56
