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).

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

So, the recursive rule for the given arithmetic sequence is

where, f(1)=84 and n ≥ 2.

Explicit rule for the arithmetic sequence is

So, the explicit rule for the given arithmetic sequence is

where, n ≥ 1.

Therefore, the recursive and explicit rules are and respectively.

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