Find the Variable Expression n for Sequence 12, 18, 24, 30, 36

Given the series whose difference between two jumped numbers is constant:

$12,18,24,30,36$

Describe the property using the variable $n$

Video Solution

Solution Steps

00:00 Find the sequence formula

00:06 This is the first term according to the given data

00:15 Let's observe the change between terms (D) according to the given data

00:27 This is the constant difference in the sequence (D)

00:30 Let's use the formula to describe the sequence

00:39 Let's substitute appropriate values and solve to find the sequence formula

00:52 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we first recognize that the sequence $12, 18, 24, 30, 36$ is an arithmetic sequence.

Step 1: Identify the first term $a_1$ .
The first term $a_1$ of the sequence is $12$ .
Step 2: Determine the common difference $d$ .
The difference between consecutive terms is consistent: $18 - 12 = 6$ . Hence, the common difference $d = 6$ .
Step 3: Formulate the expression for the general term.
The general term of an arithmetic sequence is given by $a(n) = a_1 + (n-1) \times d$ .
Step 4: Substitute the identified values into the formula.
Substituting the known values, we get $a(n) = 12 + (n-1) \times 6$ .

Thus, the expression for the general term of the given sequence is $a(n) = 12 + (n-1) \times 6$ , which corresponds to choice 3.