Summary Explanation: Finding the 5th Term of an Arithmetic Sequence

To find the 5th term of an arithmetic sequence, we can follow these steps:

Step 1: Identify the first term ($a_1$)

The first term of the sequence is given as $\frac{1}{6}$.

Step 2: Determine the common difference ($d$)

The common difference $d$ is found by subtracting the first term from the second term. For this sequence: $d = \frac{1}{3} - \frac{1}{6} = \frac{2}{6} - \frac{1}{6} = \frac{1}{6}$

Verify by subtracting the second term from the third term: $\frac{1}{2} - \frac{1}{3} = \frac{3}{6} - \frac{2}{6} = \frac{1}{6}$ So, $d = \frac{1}{6}$.

Step 3: Use the formula for the nth term

The formula for the $n$th term of an arithmetic sequence is: $a_n = a_1 + (n - 1) \times d$ Here, we want to find the 5th term ($a_5$).

Step 4: Substitute the values

Substitute $a_1 = \frac{1}{6}$, $d = \frac{1}{6}$, and $n = 5$ into the formula: $a_5 = \frac{1}{6} + (5 - 1) \times \frac{1}{6}$ $a_5 = \frac{1}{6} + 4 \times \frac{1}{6}$ $a_5 = \frac{1}{6} + \frac{4}{6} = \frac{1 + 4}{6} = \frac{5}{6}$

Step 5: Conclude the answer

The 5th term of the sequence is $\frac{5}{6}$.

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Relative Questions:

1. How do you find the common difference in an arithmetic sequence?
2. What is the formula for the nth term of an arithmetic sequence?
3. How would the process change if the common difference was negative?
4. What happens to the sequence if the common difference is zero?
5. How do you determine if a sequence is arithmetic?

Tip: Always check the common difference between consecutive terms to ensure the sequence is arithmetic.