Question

Write an explicit formula for the sequence: 3, 0, -3, -6, ...an = -3nan = 6 - 3nan = 6 + 3nan = 3n

Answer 1

Given:

The sequence is:

`3,0,-3,-6,...........`

Find-:

An explicit formula for the sequence

Explanation-:

The series is:

`3,0,-3,-6...........`

The common difference is:

`\begin{gathered} d=a_2-a_1 \\ \\ d=0-3 \\ \\ d=-3 \end{gathered}`

The n terms of A.P. series are:

`A.P.=a+(n-1)d`

The common series is:

`\begin{gathered} d=\text{ Common difference} \\ \\ a=\text{ First terms} \\ \\ a=3 \end{gathered}`
`\begin{gathered} a_n=a+(n-1)d \\ \\ a_n=3+(n-1)(-3) \\ \\ a_n=3+(-3)n+(-1)(-3) \\ \\ a_n=3-3n+3 \\ \\ a_n=6-3n \\ \end{gathered}`

So, the nth terms is:

`a_n=6-3n`