Exercise 34 Page 279

In order to write the recursive formula for the given sequence, we first need to find the common difference. We can do this by subtracting the first term of the sequence from the second term. a_2-a_1=d ⇒ 2.8-2.3= 0.5The common difference is 0.5. To write the recursive formula, we will use the general form of a recursive formula for an arithmetic sequence. A(n)=A(n-1)+d In the above formula, n is the number of the term and d is the common difference. By substituting our obtained value for d into this formula, we can create the recursive formula.

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

Substitute

d= 0.5

A(n)=A(n-1)+ 0.5

The recursive formula for the arithmetic sequence is A(n)=A(n-1)+0.5, where A(1)=2.3.