Determine the Term-to-Term Rule for the Sequence: 13, 10, 7, 4

Video Solution

Solution Steps

00:00 Find the sequence formula

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

00:12 Notice the constant difference between terms

00:19 This is the constant difference

00:26 Use the formula to describe an arithmetic sequence

00:33 Substitute appropriate values and solve to find the sequence formula

00:50 Properly expand brackets, multiply by each factor

01:01 Continue solving

01:08 And this is the solution to the question

Step-by-Step Solution

To identify the term-to-term rule of the sequence $13, 10, 7, 4, \ldots$ , let's analyze the differences between consecutive terms:

The common difference is $-3$ , confirming the sequence is arithmetic. In an arithmetic sequence, we use the formula $a_n = a_1 + (n-1) \times d$ .

Here, $a_1 = 13$ , and the common difference $d = -3$ . Plug these into the formula:

$a_n = 13 + (n-1)(-3)$

Simplify the expression:

$a_n = 13 - 3(n-1)$

$a_n = 13 - 3n + 3$

$a_n = 16 - 3n$

Thus, the term-to-term rule of the sequence is $16-3n$ . This matches choice 3 from the provided options.