Question

Help me please!!!!!!!!

Answer 1

Answer:

The sum is approximately 42.56

Step-by-step explanation:

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

$3 \, (\frac{3}{2})^0 = 3\,*\,1=3$

followed by  sum of terms of the form:

$a_1=3\,(\frac{3}{2} )^1\\a_2=3\,(\frac{3}{2} )^2\\a_3=3\,(\frac{3}{2} )^3\\a_4=3\,(\frac{3}{2} )^4\\a_5=3\,(\frac{3}{2} )^5$

and this is a geometric sequence of common ratio given by:  $\frac{3}{2}$   (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 =  $\frac{3}{2}$ , and $a$ = 3:

$S_m=a(r^m-1)/(r-1)\\S_5=3 ((\frac{3}{2})^5 -1)/(\frac{3}{2}-1)\\S_5=39.5625$

So, the total sum of the six terms is:

Total sum = 3 +39.5625 = 42.5625

which can be rounded to hundredth: 42.56