Question

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

Answer 1

8.987 (Approximate)

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
`(1)/(3)`.

So, the sum is

`6 + 2 + (2)/(3) + (2)/(9) + (2)/(27) + (2)/(81)`

=
`6 * (1 - ((1)/(3))^(6))/(1 - (1)/(3) )`

= 8.987 (Approximate) (Answer)

We know the sum of a G.P.

a + ar + ar² + ar³ + ......... up to n terms =
`a(1 - r^(n))/(1 - r)`

where -1 < r < 1.