Question

I will fan and Medal!!!! Please help if you can!
The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to represent the first three terms, respectively.] The three numbers are _____, _____, and _____.

Answer 1

\[a+aq+aq^2=-\frac{7}{10}\\a*(aq)*(aq^2)=-\frac{1}{125}\] is it ?

Answer 2

a little trick , if we use
it is simpler
\[a_1=\frac{a}{q} \\a_2=a\\a_3=aq\\now\\\frac{a}{q}+a+aq=-\frac{7}{10}\\\frac{a}{q}*a*aq=-\frac{1}{125}\rightarrow a^3=\frac{-1}{125} \rightarrow a=\frac{-1}{5}\\\]
now put a=-1/5 to other equation
and find q

Answer 3

can you go on ?

Answer 4

are you there ?

Answer 5

\[a=\frac{-1}{5}\\\frac{a}{q}+a+aq=\frac{-7}{10}\\\frac{\frac{-1}{5}}{q}+\frac{-1}{5}+\frac{-1}{5}q=\frac{-7}{10}\\\frac{1}{q}+1+q=3.5\]

Answer 6

thanks alot @amoodarya

Answer 7

your welcome