Decoding the Pattern: Determine the Term-to-Term Rule of 13, 16, 19, 22

Video Solution

Solution Steps

00:00 Find the sequence formula

00:04 Identify the first term according to the given data

00:11 Note the constant difference between terms

00:17 This is the constant difference

00:21 Use the formula to describe an arithmetic sequence

00:26 Substitute appropriate values and solve to find the sequence formula

00:38 Properly expand brackets, multiply by each factor

00:47 Continue solving

00:57 And this is the solution to the question

Step-by-Step Solution

To solve this problem, the sequence 13, 16, 19, 22 must be analyzed to find the term-to-term rule.

Step 1: Identify the common difference.

Subtract the first term from the second term:
$16 - 13 = 3$

Verify the difference throughout the sequence:
$19 - 16 = 3$
$22 - 19 = 3$

The common difference $d$ is $3$ .

Step 2: Use the arithmetic sequence formula.

Start with the general formula for an arithmetic sequence:
$a_n = a_1 + (n-1) \cdot d$

In this sequence, $a_1 = 13$ and $d = 3$ . Substitute these values in:
$a_n = 13 + (n-1) \cdot 3$

Simplify the expression:

$a_n = 13 + 3n - 3$

$a_n = 3n + 10$

The term-to-term rule of the sequence is $3n + 10$ .

Examining the given choices, the correct choice is:

$3n + 10$ (Choice 2).