Question

Write an equation to find the nth term of each sequence. See photo for rest of question.

Answer 1

13. The nth term of this sequence is
`a_n=5(4)^(n-1)` and the 9th term is 327680.

14. The nth term of this sequence is
`a_n=-2(-5)^(n-1)` and the 9th term is -781250.

In Mathematics and Geometry, the nth term of any geometric sequence can be determined by using the following formula:

`a_n=a_1(r)^(n-1)`

Where:

• 
  `a_n` is the nth term of any geometric sequence.
• r represents the common ratio.
• 
  `a_1` represents the first term of any geometric sequence.

Part 13.

Based on the given sequence, we would determine the common ratio as follows;

Common ratio, r =
`(r_2)/(r_1)`

Common ratio, r = 20/5

Common ratio, r = 4.

Therefore, the nth term and the 9th term of this sequence are given by;

`a_n=a_1(r)^(n-1)\\\\a_n=5(4)^(n-1)\\\\a_9=5(4)^(9-1)\\\\a_9=5(4)^(8)\\\\a_9=327680`

Part 14.

Based on the given sequence, we would determine the common ratio as follows;

Common ratio, r =
`(r_2)/(r_1)`

Common ratio, r = 10/-2

Common ratio, r = -5.

Therefore, the nth term and the 9th term of this sequence are given by;

`a_n=a_1(r)^(n-1)\\\\a_n=-2(-5)^(n-1)\\\\a_9=-2(-5)^(9-1)\\\\a_9=-2(-5)^(8)\\\\a_9=-781250`