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 n th term of the geometric sequence. Then find a9 .5,−10, 20,−40, …an= a9=
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.
Similar Questions
Write an equation for the $n$n th term of the geometric sequence. Then find $a_9$a9 .$1,\ 4,\ 16,\ 64,\ \ldots$1, 4, 16, 64, …$a_n=$an= $a_9=$a9=
What is the first term of a geometric sequence if its third term is −3 and its sixth term is 81?
Find a formula for the nth term of the geometric sequence. Then find the indicated nth term of the geometric sequence.15th term: 4, 8, 16,. . .
Write an equation for the $n$n th term of the arithmetic sequence. Then find $a_{30}$a30 .$-9,-6,-3,0,\ ...$−9,−6,−3,0, ...$a_n=$an= $a_{30}=$a30=
Write an equation for the nth term of the geometric sequence $7,\ 28,\ 112,\ 448,\ ...$7, 28, 112, 448, ... . Then find $a_6$a6 .An equation for the nth term of the geometric sequence is $a_n=$an= $\text{(}$( $\text{)}$) $^{n-1}$n−1 .$a_6=$a6=
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.