Question

What is the sum of the geometric sequence -1, 6, -36, . . . if there are 6 terms?

Answer 1

the formula is

Sn = a1. 1 - r^n
--------- where r = common ratio and a1 = first term
1 - r

Here we have r = -6 and a1 = -1, and n = 6. So:-

Sum of 6 terms S6 = -1 * 1 - (-6)^6
------------- = 6665
1 - (-6)

Answer 2

The sum of the given geometric sequence is -16807.

Explanation:

Since, the sum of a geometric sequence is,

`S_n=(a(r^n-1))/(r-1)` for r > 1

Or,

`S_n=(a(1-r^n))/(r-1)` for r < 1

Where, a is the first term of the sequence,

n is the number of terms

And, r is the common ratio of the sequence,

Here, the given G.P.,

-1, 6, -36,.....

So, the first term is, a = -1,

And, common ratio is,

`r=(6)/(-1)=-6 < 1`

Also, n = 6,

Hence, the sum of the given geometric sequence is,

`S_6=(-1(1-(-6))^6)/(1-(-6))`

`=-(117649)/(7)`

`=-16807`