If the 2nd term of an arithmetic progression is 15 and the 4th term is 25, what

If the 2nd term of an arithmetic progression is 15 and the 4th term is 25, what is the common difference?

If the 2nd term of an arithmetic progression is 15 and the 4th term is 25, 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 = 15.
Step 4: Write the equation for the 4th term: a + 3d = 25.
Step 5: Now you have two equations: a + d = 15 and a + 3d = 25.
Step 6: From the first equation (a + d = 15), you can express 'a' in terms of 'd': a = 15 - d.
Step 7: Substitute 'a' in the second equation (a + 3d = 25) with (15 - d): (15 - d) + 3d = 25.
Step 8: Simplify the equation: 15 - d + 3d = 25, which becomes 15 + 2d = 25.
Step 9: Solve for 'd': 2d = 25 - 15, so 2d = 10, and therefore d = 10 / 2 = 5.

Arithmetic Progression – An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant.
Common Difference – The common difference in an AP is the constant amount added to each term to get the next term.
Equations from Terms – Using the known terms of the AP to set up equations that can be solved for the first term and common difference.