If the 3rd term of an arithmetic sequence is 12 and the 7th term is 24, what is

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Question: If the 3rd term of an arithmetic sequence is 12 and the 7th term is 24, what is the common difference? (2023)

Options:

Correct Answer: 3

Exam Year: 2023

Solution:

Let the first term be a and the common difference be d. Then, a + 2d = 12 and a + 6d = 24. Solving these gives d = 3.

If the 3rd term of an arithmetic sequence is 12 and the 7th term is 24, what is the common difference? (2023)

If the 3rd term of an arithmetic sequence is 12 and the 7th term is 24, what is the common difference? (2023)

Step 1: Identify the formula for the nth term of an arithmetic sequence, which is given by the formula: a + (n-1)d, where 'a' is the first term and 'd' is the common difference.
Step 2: For the 3rd term (n=3), use the formula: a + 2d = 12. This is our first equation.
Step 3: For the 7th term (n=7), use the formula: a + 6d = 24. This is our second equation.
Step 4: Now we have two equations: a + 2d = 12 and a + 6d = 24.
Step 5: To find 'd', we can eliminate 'a' by subtracting the first equation from the second: (a + 6d) - (a + 2d) = 24 - 12.
Step 6: Simplifying this gives us: 4d = 12.
Step 7: Now, divide both sides by 4 to solve for 'd': d = 12 / 4.
Step 8: Therefore, d = 3.

Arithmetic Sequence – An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.
Solving Linear Equations – The problem requires setting up and solving a system of linear equations to find the common difference.