Question

Hello, I need help writing an explicit formula for nth term

Answer 1

Answer:
`a_(n)=4-7n`Step-by-step explanation:

The given arithmetic sequence:

-3, -10, -17, -24, .......

The common difference, d = -10 - (-3) = -10 + 3

d = -7

The first term, a = -3

Let the number of terms be n

The nth term of an arithmetic sequence is given as:

`\begin{gathered} a_n=a+(n-1)d \\ \end{gathered}`

Substitute a = -3 and d = -7 into the equation

`\begin{gathered} a_n=-3+(n-1)(-7) \\ \\ a_n=-3-7n+7 \\ \\ a_n=-3+7-7n \\ \\ a_n=4-7n \end{gathered}`

The explicit formula for the nth term is:

`a_n=4-7n`