Question

Write the recursive, arithmetic and explicit formula for the nth term of the sequence:

8, 1, -6, -13,... Then find the 10th term

Answer 1

Recursive Formula

`\begin{cases}a_1 = 8\\a_n = a_(n-1)-7\end{cases}`

The top row says the first term is 8

The bottom row says that to get the nth term, we subtract 7 from the (n-1)th term. So basically we subtract 7 from each term to get the next term.

Note the subscripts tell us which term we're working with.

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Arithmetic Formula

We have a = 8 as the first term and d = -7 as the common difference.

a(n) = a + d(n-1)

a(n) = 8 + (-7)(n-1)

a(n) = 8 - 7n + 7

a(n) = -7n+15

The nth term arithmetic formula is a(n) = -7n+15

If you plug in n = 1, you should get a(n) = 8

If you plug in n = 2, you should get a(n) = 1

and so on.

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Finding the 10th term

Plug in n = 10 to get

a(n) = -7n+15

a(10) = -7(10)+15

a(10) = -70+15

a(10) = -55

The 10th term is -55