If the 5th term of an arithmetic progression is 15 and the 10th term is 30, what

If the 5th term of an arithmetic progression is 15 and the 10th term is 30, what is the common difference?

If the 5th term of an arithmetic progression is 15 and the 10th term is 30, 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: Let the first term of the AP be 'a'. The 5th term can be expressed as a + 4d, and we know this equals 15.
Step 3: Write the equation for the 5th term: a + 4d = 15.
Step 4: The 10th term can be expressed as a + 9d, and we know this equals 30.
Step 5: Write the equation for the 10th term: a + 9d = 30.
Step 6: Now, we have two equations: a + 4d = 15 (Equation 1) and a + 9d = 30 (Equation 2).
Step 7: To find 'd', we can subtract Equation 1 from Equation 2: (a + 9d) - (a + 4d) = 30 - 15.
Step 8: Simplifying this gives us 5d = 15.
Step 9: Now, divide both sides by 5 to find d: d = 15 / 5.
Step 10: Therefore, d = 3, which is the common difference.

Arithmetic Progression – An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant.
Term Calculation – The nth term of an AP can be calculated using the formula: T_n = a + (n-1)d, where a is the first term and d is the common difference.
System of Equations – The problem involves solving a system of linear equations to find the values of a and d.