If the 2nd term of an arithmetic progression is 10 and the 5th term is 16, what

If the 2nd term of an arithmetic progression is 10 and the 5th term is 16, what is the common difference?

If the 2nd term of an arithmetic progression is 10 and the 5th term is 16, 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 2nd term: a + d = 10.
Step 4: Write the equation for the 5th term: a + 4d = 16.
Step 5: Now you have two equations: a + d = 10 and a + 4d = 16.
Step 6: From the first equation (a + d = 10), you can express 'a' in terms of 'd': a = 10 - d.
Step 7: Substitute 'a' in the second equation: (10 - d) + 4d = 16.
Step 8: Simplify the equation: 10 - d + 4d = 16 becomes 10 + 3d = 16.
Step 9: Solve for 'd': 3d = 16 - 10, which simplifies to 3d = 6.
Step 10: Divide both sides by 3 to find d: d = 6 / 3, which gives d = 2.

Arithmetic Progression – Understanding the properties of arithmetic sequences, including how to derive terms based on the first term and common difference.
Algebraic Manipulation – Solving linear equations to find unknown variables.