Question

for the sequence, describe the pattern, write the next term, and write a rule for the nth term 1.) 2,4,8,16 2.)1,8,27,64 3.)1/1,1/4,1/9,1/16 4.)4/3,5/3,6/3,7/3 5.)3,5,7,9

Answer 1

1. Powers of 2 (
`2^1=2,\,2^2=4,\,2^3=8,\,2^4=16,\ldots`).

Next term =
`2^5=\boxed{32}`


`\boxed{a_n=2^n}`

2. Cube numbers (
`1^3=1,\,2^3=8,\,3^3=27,\,4^3=64,\ldots`)

Next term =
`5^3=\boxed{125}`


`\boxed{a_n=n^3}`

3. Reciprocals of the square numbers (
`(1)/(1^2)=(1)/(1),\,(1)/(2^2)=(1)/(4),\,(1)/(3^2)=(1)/(9),\,(1)/(4^2)=(1)/(16),\ldots`

Next term =
`(1)/(5^2)=\boxed{(1)/(25)}`


`\boxed{a_n=(1)/(n^2)}`

4. Numbers 4, 5, 6, 7,... divided by 3.

Next term =
`(8)/(3)`


`\boxed{a_n=(n+3)/(3)}`

5. Odd numbers from 3.

Next term = 11


`\boxed{a_n=2n+1}`