Answered

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What is the 9th term of a geometric
sequence with a first term of 12 and a
common ratio of -3?

Sagot :

Luv2Teach

Answer:

Step-by-step explanation:

The formula for an explicit geometric sequence is

[tex]a_n=a_1*r^{n-1[/tex] where n is the position of the number in the sequence (ours will be 9 since we are looking for the 9th term), a1 is the first term in the sequence (ours is given as 12), and r is the common ratio (ours is given as -3). Filling all of that in to get the explicit formula we need:

[tex]a_n=12*(-3)^{n-1[/tex] and solving for the 9th term:

[tex]a_9=12*(-3)^8[/tex] which gives us, simplified a bit:

[tex]a_9=12(6561)[/tex] so

a9 = 78,732

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