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?

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Q: 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?

Solution: In an arithmetic series, the last term can be expressed as a + (n-1)d. Here, 48 = 12 + (10-1)d. Thus, 48 - 12 = 9d, giving d = 4.

Steps: 10

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.