Question

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

Answer 1

Answer:

The sum of the given geometric sequence is -16807.

Step-by-step explanation:

Since, the sum of a geometric sequence is,

$S_n=\frac{a(r^n-1)}{r-1}$ for r > 1

Or,

$S_n=\frac{a(1-r^n)}{r-1}$ 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,

$r=\frac{6}{-1}=-6 < 1$

Also, n = 6,

Hence, the sum of the given geometric sequence is,

$S_6=\frac{-1(1-(-6))^6}{1-(-6)}$

$=-\frac{117649}{7}$

$=-16807$

Answer 2

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)