Exercise 78 Page 273

Let's start by writing the explicit formula. Examining the sequence, we notice that this is an arithmetic sequence.

3

and the sequence has a starting value of

5 .

With this information we can write the sequence's explicit formula.

t (n) = 3 (n - 1) + 5 Slope : 3 First Term : 5

Let's simplify this equation.

t (n) = 3 (n - 1) + 5

Distribute $3$

t (n) = 3 n - 3 + 5

Add terms

t (n) = 3 n + 2

A recursive formula requires the previous term to find an arbitrary term in the sequence. It can be written in the following general format.

t (n + 1) = t (n) + m, t (1) = a

From the exercise, we know that

m = 3

and the first term is

5 .

Now we can write the recursive formula.

t (n + 1) = t (n) + 3, t (1) = 5