If the first term of an arithmetic progression is 4 and the sum of the first 6 t

If the first term of an arithmetic progression is 4 and the sum of the first 6 terms is 60, what is the common difference?

If the first term of an arithmetic progression is 4 and the sum of the first 6 terms is 60, what is the common difference?

Step 1: Identify the first term (a) of the arithmetic progression, which is given as 4.
Step 2: Identify the number of terms (n) we are summing, which is given as 6.
Step 3: Identify the sum of the first 6 terms (S_n), which is given as 60.
Step 4: Use the formula for the sum of the first n terms of an arithmetic progression: S_n = n/2 * (2a + (n-1)d).
Step 5: Substitute the known values into the formula: 60 = 6/2 * (2*4 + (6-1)d).
Step 6: Simplify the equation: 60 = 3 * (8 + 5d).
Step 7: Divide both sides by 3: 20 = 8 + 5d.
Step 8: Subtract 8 from both sides: 12 = 5d.
Step 9: Divide both sides by 5 to find d: d = 12/5.
Step 10: Simplify 12/5 to get d = 2.4.

Arithmetic Progression – An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant.
Sum of an Arithmetic Series – The sum of the first n terms of an arithmetic series can be calculated using the formula S_n = n/2 * (2a + (n-1)d), where a is the first term and d is the common difference.