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For a given geometric sequence, the common ratio, r, is equal to 5, and the 7th term, an, is equal to -43. Find the value of the 9thterm, a9. If applicable, write your answer as a fraction.a9=

For A Given Geometric Sequence The Common Ratio R Is Equal To 5 And The 7th Term An Is Equal To 43 Find The Value Of The 9thterm A9 If Applicable Write Your Ans class=

Sagot :

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.

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