Question

Complete the recursive rule and the explicit rule for the arithmetic sequence. 84, 94, 104, 114, 124,.... The recursive rule is f(1) = , f(n) = f(n − 1) + for n ≥ 2. The explicit rule is f(n) = + (n − 1).

Answer 1

Given:

The arithmetic sequence is

84, 94, 104, 114, 124,....

To find:

The recursive rule and the explicit rule for the arithmetic sequence.

Solution:

We have, the arithmetic sequence

84, 94, 104, 114, 124,....

Here,

First term : a=84

Common difference : d=94-84=10

The recursive rule for an arithmetic sequence is

`f(n)=f(n-1)+d`

So, the recursive rule for the given arithmetic sequence is

`f(n)=f(n-1)+10`

where, f(1)=84 and n ≥ 2.

Explicit rule for the arithmetic sequence is

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

So, the explicit rule for the given arithmetic sequence is

`f(n)=84+(n-1)10`

where, n ≥ 1.

Therefore, the recursive and explicit rules are
`f(n)=f(n-1)+10` and
`f(n)=84+(n-1)10` respectively.