Question

6+2+2/3+2/9+...+a6 evaluate

Answer 1

Answer:

8.987 (Approximate)

Step-by-step explanation:

We have to find the sum of a G.P. series up to sixth terms.

The first term of the series is 6 and common ratio is $\frac{1}{3}$.

So, the sum is  

$6 + 2 + \frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81}$

= $6 \times \frac{1 - (\frac{1}{3})^{6}}{1 - \frac{1}{3} }$

= 8.987 (Approximate) (Answer)

We know the sum of a G.P.

a + ar + ar² + ar³ + ......... up to n terms = $a\frac{1 - r^{n}}{1 - r}$  

where -1 < r < 1.