3. Given the recursive equation for each arithmetic sequence, write the explicit equation. f(n)=f(n-1)-2; f(1)=8
f(n)=5+f(n-1);f(1)=0

Given:

The recursive formulae are:

(a)

(b)

To find:

The explicit equation.

Solution:

A recursive formula of an arithmetic sequence is

and f(1) is the first term.

Where, d is the common difference.

The explicit formula is

where, a is first term and d is common difference.

(a)

We have,

Here, first term is 8 and common difference is -2. So, the explicit formula is

Therefore, the explicit formula is .

(b)

We have,

Here, first term is 0 and common difference is 5. So, the explicit formula is

Therefore, the explicit formula is .

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