Question

Explicit formula fir this sequence?

Answer 1

`\displaystyle{a_n=-3n+12}`

Explanation:

From:

`\displaystyle{a_n = a_(n-1) -3}`

We can isolate -3, so we have:

`\displaystyle{a_n - a_(n-1)= -3}`

We know that if a next term subtracts a previous term, it forms a difference. If we keep subtracting and we still have same difference, it's a common difference of a sequence. Thus,

`\displaystyle{d= -3}`

Where d is a common difference. Then apply the arithmetic sequence formula where:

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

Substitute the known values:

`\displaystyle{a_n = 9+(n-1)(-3)}\\\\\displaystyle{a_n = 9-3n+3}\\\\\displaystyle{a_n=-3n+12}`