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