Question

What the explicit formula of 3 5 7 9

Answer 1

`a_(n)=3+2(n-1)`

Explanation:

Given:

The given sequence is 3, 5, 7, 9

The difference between the second and first term is 5 - 3 = 2

The difference between the third and second term is 7 - 5 = 2

The difference between the fourth and third term is 9 - 7 = 2

So, there is a common difference of 2. Thus a sequence which has the same difference is known as an arithmetic sequence.

The explicit formula to determine the
`n^(th)` term of an arithmetic sequence is given as:

`a_n=a_1+(n-1)d`

Where,
`a_1\rightarrow 1^(st)\ term, d\rightarrow \textrm{common difference}`

Plug in 3 for
`a_1` and 2 for
`d`. This gives,

`a_(n)=3+(n-1)* 2`

Therefore, the explicit formula to represent the given sequence is:

`a_(n)=3+2(n-1)`