Question

Write an explicit formula for an arithmetic sequence whose common difference is -3, and first term is -9.

Answer 1

The required formula is
`a_n =-3n-6`.

Explanation:

Given : An arithmetic sequence whose common difference is -3, and first term is -9.

To find : Write an explicit formula for an arithmetic sequence ?

Solution :

An explicit formula for an arithmetic sequence is given by,
`a_n = a_1 +d(n -1)`

Where,
`a_n` is the nth term of the sequence

`a_1=-9` is the first term of the sequence

d=-3 is the common difference

n is the number terms

Substitute the value in the formula,

`a_n =(-9)+(-3)(n -1)`

`a_n =-9-3n+3`

`a_n =-3n-6`

Therefore, the required formula is
`a_n =-3n-6`.

Answer 2

an = -9 -3(n -1)

Explanation:

The explicit formula for an arithmetic sequence with first term a1 and common difference d is ...

an = a1 +d(n -1)

Putting your numbers into the formula gives ....

an = -9 -3(n-1)