Find the 12th term of the arithmetic sequence 5, 9, 13, 17, ...

Solution

Precalculus · Easy

Step 1: Identify the first term and common difference.

The sequence is:
5, 9, 13, 17, ...

The first term is:
a₁ = 5

Find the common difference by subtracting consecutive terms:
9 - 5 = 4
13 - 9 = 4

So the common difference is:
d = 4

Step 2: Use the formula for the nth term of an arithmetic sequence.

The formula is:
aₙ = a₁ + (n - 1)d

Step 3: Substitute n = 12, a₁ = 5, and d = 4.

a₁₂ = 5 + (12 - 1)(4)

Step 4: Simplify.

a₁₂ = 5 + 11(4)

a₁₂ = 5 + 44

a₁₂ = 49

Therefore, the 12th term of the sequence is 49.

Result

49