What is the sum of the geometric sequence -1, 6, -36, ... if there are 7 terms?

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Answer 1 · 2015-09-02T10:14:46

#S_7=-39991#

In this sequence we have: #a_1=-1#, #q=-6#, #n=7#. If we apply the formula for #S_n# we get:

#S_7=(-1)*(1-(-6)^7)/(1-(-6))#

#S_7=(-1)*(1+279936)/7#

#S_7=-39991#

Answer 2 · 2016-08-20T12:04:53

#S_n = -39,991#

In the given GP, we have the following:

#a_1 = -1, and n = 7#

We can find #r = 6/-1 =-36/6= -6#

There are 2 formulae for #S_n# depending on whether r is a proper fraction or not.

#S_n = (a(r^n - 1))/(r-1)" substitute with the values"#

#S_n = (-1((-6)^7 - 1))/(-6-1)#

#S_n = (-1(-279,937))/(-7)#

#S_n = -39,991#