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Core Connections Integrated I, 2014

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Core Connections Integrated I, 2014 View details

2. Section 5.2

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Exercise 78 Page 273

Pay attention to how the sequence is changing to look for an equation that describes its behavior.

Explicit Formula: $t (n) = 3 n + 2$
Recursive Formula: $t (n + 1) = t (n) + 3,$ $t (1) = 5$

Practice makes perfect

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

As we can see, the common difference is

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

Subchapter links

5.2.1 Generating and Investigating Sequences p.264-265

5.2.2 Generalizing Arithmetic Sequences p.269-270

5.2.3 Recursive Sequences p.273-274