Question

If the sequence is 5,8,12.8, 20.48, is the sequence arithmetic or geometric? What is the general term? What is the seventh term?

Answer 1

the common ratio is 5/8 for the given sequence.

Would you like to suggest the next number?

Explanation:

Answer 2

a) The sequence is geometric

b)
`t_n=5* \left ((8)/(5) \right )^(n-1)`

c) Seventh term = 83.88608

Explanation:

If it is an arithmetic progression common difference will be same,

8 - 5 = 3

12.8 - 8 = 4.8

Since common difference is not same the numbers are not arithmetic.

If it is an geometric progression common ration will be same,

`(8)/(5)\\\\(12.8)/(8)=(8)/(5)\\\\(20.48)/(12.8)=(8)/(5)`

Since common ratio is same the numbers are geometric.

b) General term of GP is given by

`t_n=ar^(n-1)=5* \left ((8)/(5) \right )^(n-1)\\\\t_n=5* \left ((8)/(5) \right )^(n-1)`

c) Seventh term means n = 7

`t_7=5* \left ((8)/(5) \right )^(7-1)=5* \left ((8)/(5) \right )^(6)=83.88608`

Seventh term = 83.88608