In an arithmetic progression, if the 3rd term is 12 and the 7th term is 24, what

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Question: In an arithmetic progression, if the 3rd term is 12 and the 7th term is 24, what is the common difference?

Options:

Correct Answer: 4

Solution:

Let the first term be a and the common difference be d. From the equations a + 2d = 12 and a + 6d = 24, we can find d = 3.

In an arithmetic progression, if the 3rd term is 12 and the 7th term is 24, what is the common difference?

In an arithmetic progression, if the 3rd term is 12 and the 7th term is 24, what is the common difference?

Step 1: Understand that in an arithmetic progression, each term is found by adding a common difference to the previous term.
Step 2: Let the first term be 'a' and the common difference be 'd'.
Step 3: Write the equation for the 3rd term: a + 2d = 12.
Step 4: Write the equation for the 7th term: a + 6d = 24.
Step 5: Now you have two equations: a + 2d = 12 and a + 6d = 24.
Step 6: Solve the first equation for 'a': a = 12 - 2d.
Step 7: Substitute 'a' in the second equation: (12 - 2d) + 6d = 24.
Step 8: Simplify the equation: 12 + 4d = 24.
Step 9: Solve for 'd': 4d = 24 - 12, which means 4d = 12.
Step 10: Divide both sides by 4 to find 'd': d = 12 / 4, so d = 3.

Arithmetic Progression – An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant.
Terms of an Arithmetic Sequence – The nth term of an arithmetic sequence can be expressed as a + (n-1)d, where a is the first term and d is the common difference.
Solving Linear Equations – The problem requires solving a system of linear equations to find the values of a and d.