Question

find the 15th term of this arithmetic sequence.

2, 10, 18, 26, 34, ...

\\(a_{15} = ? \\)

hint: \\(a_n = a_1 + (n - 1)d\\)

Explanation:

Identify the sequence parameters

We are given the arithmetic sequence:

$$ 2, 10, 18, 26, 34, \dots $$

The first term \(a_1\) is:

$$ a_1 = 2 $$

The common difference \(d\) is the difference between any two consecutive terms:

$$ d = 10 - 2 = 8 $$

State the target term

We want to find the 15th term of this sequence.
This means we set:

$$ n = 15 $$

Apply the arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is:

$$ a_n = a_1 + (n - 1)d $$

Substituting our known values:

$$ a_{15} = 2 + (15 - 1) \cdot 8 $$

Calculate the final value

Simplify the expression inside the parentheses first:

$$ a_{15} = 2 + 14 \cdot 8 $$

Multiply 14 by 8:

$$ 14 \cdot 8 = 112 $$

Add the first term:

$$ a_{15} = 2 + 112 = 114 $$

Answer:

Find the 15th term of this arithmetic sequence.

\(2, 10, 18, 26, 34, \dots\)

\(a_{15} =\) <blank>114</blank>

Hint: \(a_n = a_1 + (n - 1)d\)