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

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Q: In an arithmetic progression, if the first term is 12 and the last term is 48, and there are 10 terms, what is the common difference?

Solution: Using the formula for the last term, 48 = 12 + (10-1)d. Solving gives d = 4.

Steps: 9

Step 1: Identify the first term (a) of the arithmetic progression, which is given as 12.
Step 2: Identify the last term (l) of the arithmetic progression, which is given as 48.
Step 3: Identify the number of terms (n) in the arithmetic progression, which is given as 10.
Step 4: Use the formula for the last term of an arithmetic progression: l = a + (n - 1)d.
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: 48 - 12 = 9d, which simplifies to 36 = 9d.
Step 8: Divide both sides by 9 to find d: d = 36 / 9.
Step 9: Calculate the value of d: d = 4.