Question 1154282

first we need nth term formula:

write given terms as follow:

{{{-3=3*(-1)^1*5^0}}}

{{{15=3*(-1)^(2)*5^1}}}

{{{ -75=3*(-1)^3*5^2}}}

{{{375=3*(-1)^4*5^3}}}
:
in general

{{{3 (-1)^n *5^(n - 1)}}}

5th term

{{{3 (-1)^5 *5^(5 - 1)=3 (-1)^5 *5^4=-1875}}}

6th term

{{{3 (-1)^6 *5^(6 - 1)=3 (-1)^6 *5^5=9375}}}

7th term

{{{3 (-1)^7 *5^(7 - 1)=3 (-1)^7 *5^6=-46875}}}


the sum of the first {{{7}}} terms geometric sequence is:

{{{ -3+ 15 -75+375-1875+9375-46875=-39063}}}