Given:
it is given that common ration of a geometric sequence is r = 5 and 7th term is - 43.
Find:
we have to find the value of 9th term.
Explanation:
we know the formula for nth term of a geometric sequence is
[tex]a_n=ar^{n-1}[/tex]
since, 7the term is - 43,
Therefore, we have
[tex]\begin{gathered} a_7=-43 \\ ar^{7-1}=-43 \\ ar^6=-43 \\ a(5)^6=-43 \\ a(15625)=-43 \\ a=-\frac{43}{15625} \end{gathered}[/tex]
The 9the term of the geometric sequence is
[tex]\begin{gathered} a_9=-\frac{43}{15625}\times(5)^{9-1} \\ =-\frac{43}{15625}\times(5)^8 \\ =-\frac{43}{(5)^6}\times(5)^8 \\ =-43\times25 \\ a_9=-1075 \end{gathered}[/tex]
Therefore, 9th term of given geometric sequence is -1075.
