# How do you find the sum of the finite geometric sequence of sum_(n=0)^5 300(1.06)^n?

Jul 12, 2018

#### Answer:

${\sum}_{n = 0}^{5} 300 {\left(1.06\right)}^{n} \approx 2092.6$

#### Explanation:

This is geometric sequence of which $1$ st term is $a = 300$,

common ration is $r = 1.06$ and number of terms is $n = 6$

Sum is ${s}_{n} = \frac{a \left({r}^{n} - 1\right)}{r - 1} = \frac{300 \left({1.06}^{6} - 1\right)}{1.06 - 1}$

$\therefore {s}_{n} \approx 2092.6 \therefore {\sum}_{n = 0}^{5} 300 {\left(1.06\right)}^{n} \approx 2092.6$ [Ans]