Find the Variable Expression for Sequence: 3, 8.5, 14, 19.5, 25

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

$3,8.5,14,19.5,25$

Describe the property using the variable $n$

Video Solution

Solution Steps

00:00 Find the sequence formula

00:04 This is the first term according to the given data

00:08 Let's observe the change between terms (D) according to the given data

00:29 We'll use the formula to describe the sequence

00:37 We'll substitute appropriate values and solve to find the sequence formula

00:51 And this is the solution to the question

Step-by-Step Solution

To solve this problem, let's derive the formula for the arithmetic sequence:

Step 1: Identify the first term $a_1$ . In this series, the first term is $3$ .
Step 2: Determine the common difference $d$ . By calculation, the difference between each consecutive term is constant at $5.5$ .
Step 3: Use the common formula for an arithmetic sequence: $a(n) = a_1 + (n-1) \cdot d$ .
Step 4: Substitute the values into the formula: $a(n) = 3 + (n-1) \cdot 5.5$ .

Applying these steps confirms the general term for this arithmetic sequence is:

$a(n) = 3 + (n-1) \times 5.5$

Thus, the correct formulation for $n$ -th term of the sequence is given by this expression.

Therefore, the correct answer is choice 3: $a(n)=3+(n-1)\times5.5$ .