If the first term of an arithmetic series is 12 and the last term is 48, what is

If the first term of an arithmetic series is 12 and the last term is 48, what is the common difference if there are 10 terms?

If the first term of an arithmetic series is 12 and the last term is 48, what is the common difference if there are 10 terms?

Step 1: Identify the first term of the arithmetic series, which is given as 12.
Step 2: Identify the last term of the arithmetic series, which is given as 48.
Step 3: Identify the number of terms in the series, which is given as 10.
Step 4: Use the formula for the last term of an arithmetic series: last term = first term + (number of terms - 1) * common difference.
Step 5: Substitute the known values into the formula: 48 = 12 + (10 - 1) * d.
Step 6: Simplify the equation: 48 = 12 + 9d.
Step 7: Subtract 12 from both sides to isolate the term with d: 48 - 12 = 9d.
Step 8: Calculate the left side: 36 = 9d.
Step 9: Divide both sides by 9 to solve for d: d = 36 / 9.
Step 10: Calculate the value of d: d = 4.

Arithmetic Series – An arithmetic series is a sequence of numbers in which the difference between consecutive terms is constant.
Common Difference – The common difference is the fixed amount added to each term to get to the next term in an arithmetic series.
Formula for the Last Term – The last term of an arithmetic series can be calculated using the formula: last term = first term + (n-1) * common difference.