Respuesta :

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:

The sum of the given geometric sequence is -16807.

Step-by-step explanation:

Since, the sum of a geometric sequence is,

[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex] for r > 1

Or,

[tex]S_n=\frac{a(1-r^n)}{r-1}[/tex] 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,

[tex]r=\frac{6}{-1}=-6 < 1[/tex]

Also, n = 6,

Hence, the sum of the given geometric sequence is,

[tex]S_6=\frac{-1(1-(-6))^6}{1-(-6)}[/tex]

[tex]=-\frac{117649}{7}[/tex]

[tex]=-16807[/tex]

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