Question #254f6

2 Answers
Oct 7, 2017

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

Oct 7, 2017

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!!