Question

Question #254f6

Answer 1

`S_7=1094`

Explanation:

`"the "color(blue)"sum to n terms"` for a geometric series is.

`•color(white)(x)S_n=(a(r^n-1))/(r-1)`

`"where a is the first term and r the "color(blue)"common ratio"`

`r=(a_2)/(a_1)=(-6)/2=-3`

`rArrS_7=(2((-3)^7-1))/(-4)`

`color(white)(rArrS_7)=(2xx-2188)/(-4)=1094`

Answer 2

Answer is `1094`.

Explanation:

Given the geometric series is:

`color(red)(2-6+18-54.......)` up to `7^(th)` term.

Let, `t_1=a=2`
`t_2=a_1=-6`.

So, common multiplier
`color(red)(=t_2/t_1=a_2/a=-6/2=-3)`
`:.r=-3`

Now, Let a term of the sequence be `t_n`.
`:.t_n=a.r^(n-1)`
So, `t_7=2.(-3)^(7-1)`
`:.color(red)(t_7=2.3^6=1485)`.

Now, Let sum of the series up to `n` terms be `S_n`.

`S_n=(a(r^n-1))/(r-1)`.
`:.S_7=2[(-3)^7-1]/(-3-1)`.
`:.S_7=2xx2188/4=1094`.

So, sum upto `7th` term of the sequence is `1094`. (Answer).

Hope it Helps!!