Question

functions and lines
finding a specified term of an arithmetic sequence given the first terms
find the 76^th term of the following arithmetic sequence.
14, 22, 30, 38, ...

Explanation:

Step1: Identify the formula for the nth term of an arithmetic sequence

The formula for the nth term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \), where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

Step2: Find the first term (\( a_1 \)) and the common difference (\( d \))

For the given sequence \( 14, 22, 30, 38, \dots \), the first term \( a_1 = 14 \).
To find the common difference \( d \), subtract the first term from the second term: \( d = 22 - 14 = 8 \).

Step3: Substitute the values into the formula to find the 76th term

We need to find the 76th term, so \( n = 76 \), \( a_1 = 14 \), and \( d = 8 \).
Substitute these values into the formula:

$$
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$$

Answer:

614