Question

Write an explicit formula for an arithmetic sequence whose common difference is -4.5

Answer 1

The explicit formula for an arithmetic sequence whose common difference is -4.5 is:

`a_n=a_1-4.5(n-1)`

Explanation:

Explicit formula--

Explicit formula is the formula which is used to find the nth term of a sequence.

We know that the explicit formula for an arithmetic sequence is given by:

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

where d is the common difference of the sequence and
`a_1` is the first term of the sequence.

We have: d= -4.5

Hence, the explicit formula is given by:

`a_n=a_1-4.5(n-1)`

Answer 2

For this case we have:

The general formula of the arithmetic sequence is given by:

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

Where

`a_n`: Last term

`a_1`: First term

n: Number of terms

d: Difference

Rewriting according to the given common difference, we have:

`a_n = a_1 + (n-1) (- 4.5)`

Answer:

`a_n = a_1 + (n-1) (- 4.5)`