If the 3rd term of an arithmetic progression is 15 and the 6th term is 24, what

If the 3rd term of an arithmetic progression is 15 and the 6th term is 24, what is the common difference?

If the 3rd term of an arithmetic progression is 15 and the 6th term is 24, what is the common difference?

Step 1: Understand that in an arithmetic progression (AP), each term is found by adding a common difference (d) to the previous term.
Step 2: Identify the terms given in the problem. The 3rd term is 15 and the 6th term is 24.
Step 3: Write the formula for the 3rd term. The 3rd term can be expressed as: a + 2d = 15, where 'a' is the first term.
Step 4: Write the formula for the 6th term. The 6th term can be expressed as: a + 5d = 24.
Step 5: Now you have two equations: a + 2d = 15 and a + 5d = 24.
Step 6: Solve the first equation for 'a': a = 15 - 2d.
Step 7: Substitute 'a' from Step 6 into the second equation: (15 - 2d) + 5d = 24.
Step 8: Simplify the equation: 15 + 3d = 24.
Step 9: Solve for 'd': 3d = 24 - 15, which simplifies to 3d = 9.
Step 10: Divide both sides by 3 to find 'd': d = 9 / 3, which gives d = 3.

Arithmetic Progression – An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant.
Equations – The problem involves setting up and solving linear equations based on the properties of an arithmetic progression.