Given geometric sequence = -3,15,-75,375,....
Common ratio = r = [tex]\frac{15}{-3} = -5[/tex]
[tex]S_{n}= a\left ( \frac{1-r^{n}}{1 - r} \right )[/tex]
To find the sum of seven terms,
n = number of terms = 7
a = 1st term = -3
r = common ratio = -5
[tex]S_{7}= (-3)\left ( \frac{1-(-5)^{7}}{1 - (-5)} \right )[/tex]
[tex]S_{7}= (-3)\left ( \frac{1+78125}{1 + 5} \right )[/tex]
[tex]S_{7}= (-3)\left ( \frac{78126}{6} \right )[/tex]
[tex]S_{7}= (-3)\times 13021[/tex]
[tex]S_{7}[/tex] = - 39063
Sum of 7 terms of the geometric sequence = - 39063
