If the 6th term of an arithmetic progression is 30 and the 9th term is 45, what

If the 6th term of an arithmetic progression is 30 and the 9th term is 45, what is the common difference?

If the 6th term of an arithmetic progression is 30 and the 9th term is 45, 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 formula for the nth term of an AP, which is given by: nth term = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.
Step 3: For the 6th term, set up the equation: a + 5d = 30.
Step 4: For the 9th term, set up the equation: a + 8d = 45.
Step 5: Now you have two equations: a + 5d = 30 and a + 8d = 45.
Step 6: To eliminate 'a', subtract the first equation from the second: (a + 8d) - (a + 5d) = 45 - 30.
Step 7: Simplify the equation: 3d = 15.
Step 8: Solve for d by dividing both sides by 3: d = 15 / 3 = 5.

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.