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Write an equation for the $n$n​ th term of the geometric sequence. Then find $a_9$a9​​ .$5,-10,\ 20,-40,\ \ldots$5,−10, 20,−40, …​$a_n=$an​=​  $a_9=$a9​=​

Question

Write an equation for the nn th term of the geometric sequence. Then find a9a_9.

The geometric sequence is:
5,10,20,40,ldots5, -10, 20, -40, \\ldots

  1. an=a_n =
  2. a9=a_9 =
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Solution

The general formula for the nth term of a geometric sequence is:

a_n = a_1 * r^(n-1)

where:

  • a_n is the nth term
  • a_1 is the first term
  • r is the common ratio
  • n is the term number

In this sequence, the first term a_1 is 5 and the common ratio r is -2 (since each term is -2 times the previous term).

So, the nth term of the sequence can be written as:

a_n = 5 * (-2)^(n-1)

To find the 9th term a_9, we substitute n = 9 into the formula:

a_9 = 5 * (-2)^(9-1) a_9 = 5 * (-2)^8 a_9 = 5 * 256 a_9 = 1280

So, the 9th term of the sequence is 1280.

This problem has been solved

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