Question

Create three geometric sequences of your own (including one that is decreasing). Extend your sequences to include five terms. Then, identify the order of each term and the common ratio. Type your work in the text box below.

Answer 1

a)
`a_n=5\,\,(2)^(n-1)`

b)
`b_n=100\,\,((1)/(2) )^(n-1)`

c)
`c_n=160\,\,(-(1)/(2) )^(n-1)`

Explanation:

a) Geometric sequence with first term 5 and common ratio 2, where the nth term can be calculated via:

`a_n=5\,\,(2)^(n-1)`

The first five terms are:
`a_1=5;\,\,\,a_2=10;\,\,\,a_3=20; \,\,\,a_4=40;\,\,\,a_5=80`

b) Geometric sequence with first term 100 and common ratio 1/2, where the nth term can be calculated via:

`b_n=100\,\,((1)/(2) )^(n-1)`

The first five terms are:
`a_1=100;\,\,\,a_2=50;\,\,\,a_3=25; \,\,\,a_4=12.5;\,\,\,a_5=6.25`

c) Geometric sequence with first term 160 and common ratio -1/2, where the nth term can be calculated via:

`c_n=160\,\,(-(1)/(2) )^(n-1)`

The first five terms are:
`a_1=160;\,\,\,a_2=-80;\,\,\,a_3=40; \,\,\,a_4=-20;\,\,\,a_5=10`