Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n)=5+(n-1)( (1)/(6) ) three answers

Question

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.


`A(n)=5+(n-1)( (1)/(6) )`

three answers

Answer 1

`A(1)=5+(1-1)((1)/(6))=5+0((1)/(6))=5+0=5`

`A(14)=5+(5-1)((1)/(6))=5+4((1)/(6))=5+(4)/(6)=5(2)/(3)`

`A(10)=5+(10-1)((1)/(6))=5+9((1)/(6))=5+(9)/(6)=6(1)/(2)`

Answer 2

The first term is
`A(1)=5`

The fourth term is
`A(4)=(11)/(2)`.

The tenth term is
`A(10)=(13)/(2)`

Explanation:

Given : Arithmetic sequence
`A(n)=5+(n-1)( (1)/(6) )`

To find : The first, fourth, and tenth terms of the arithmetic sequence described by the given rule?

Solution :

Arithmetic sequence
`A(n)=5+(n-1)((1)/(6))`

Substitute, n=1,4,10 to find the given terms

Put n=1,

`A(1)=5+(1-1)((1)/(6))`

`A(1)=5+(0)((1)/(6))`

`A(1)=5`

The first term is
`A(1)=5`

Put n=4,

`A(4)=5+(4-1)((1)/(6))`

`A(4)=5+(3)((1)/(6))`

`A(4)=5+(1)/(2)`

`A(4)=(11)/(2)`

The fourth term is
`A(4)=(11)/(2)`.

Put n=10,

`A(10)=5+(10-1)((1)/(6))`

`A(10)=5+(9)((1)/(6))`

`A(10)=5+(3)/(2)`

`A(10)=(13)/(2)`

The tenth term is
`A(10)=(13)/(2)`