Question

Consider the first four terms of an arithmetic sequence below. 7, 13, 19, 25 Determine the recursive and explicit formulas that describe this sequence. The recursive function that describes this sequence is f(1) = 7, f(n-1) {+7,+6,+1,+13}, n≥2. The explicit function that describes this situation is f(n) = {1,6,13,7} and f(10) = {61,59,69,71}.

Answer 1

The first four terms in an arithmetic sequence are ;

7,13,19,25,

The recursive formula will allow you to determine any term of the arithmetic sequence

In this case, find the common difference as

13-7 = 6

The first term is given as;

`a_(n=)a_{n-1\text{ }}+\text{ d , n}\ge2`

Given the first term and the common difference , 6, substitute these in the formula as;

an= a1 + d{n-1}

= 7 + 6{n-1}

= 7 + 6n -6

an= 6n + 1 ---------explicit formula

For the recursive formula

`a_{1\text{ = 7}}`

The common difference is =6

Then ;

`a_(n=)a_{n-1+\text{ 6 , n}\ge2}`