In an arithmetic progression, if the 3rd term is 15 and the 6th term is 24, what

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Question: In an arithmetic progression, if the 3rd term is 15 and the 6th 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 = 15 and a + 5d = 24, we can solve for d, which gives d = 3.

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

In an arithmetic progression, if the 3rd term is 15 and the 6th 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 = 15.
Step 4: Write the equation for the 6th term: a + 5d = 24.
Step 5: Now you have two equations: a + 2d = 15 and a + 5d = 24.
Step 6: To find 'd', first solve for 'a' in terms of 'd' from the first equation: a = 15 - 2d.
Step 7: Substitute 'a' in the second equation: (15 - 2d) + 5d = 24.
Step 8: Simplify the equation: 15 + 3d = 24.
Step 9: Solve for 'd': 3d = 24 - 15, which gives 3d = 9.
Step 10: Divide by 3 to find d: d = 9 / 3, which gives d = 3.

Arithmetic Progression – Understanding the properties of arithmetic sequences, including how to derive terms based on the first term and common difference.
Solving Linear Equations – Ability to set up and solve equations based on given conditions to find unknown variables.