Question

Evaluate the finite series for the specified number of terms.

Answer 1

Since it is a geometric sequence is given by:

`\begin{gathered} a_n=a1\cdot r^(n-1) \\ _{\text{ }}where\colon \\ a1=81 \\ a2=27 \\ so\colon \\ 27=81r \\ r=(27)/(81) \\ r=(1)/(3) \\ _{\text{ }}hence\colon \\ a_n=81((1)/(3))^(n-1) \end{gathered}`

The sum is given by:

`S_(180)=\sum ^(180)_(n\mathop=1)81((1)/(3))^(n-1)=\frac{a1(r^n^{}-1)}{r^{}-1}=(81((1)/(3)^(180)-1))/((1)/(3)-1)=121.5`

Answer:

121.5