In an arithmetic series, if the first term is 5 and the last term is 45, and there are 10 terms, what is the common difference?

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Q: In an arithmetic series, if the first term is 5 and the last term is 45, and there are 10 terms, what is the common difference?

Solution: Using the formula for the nth term: a_n = a + (n-1)d, we have 45 = 5 + 9d. Solving gives d = 4.

Steps: 9

Step 1: Identify the first term (a) of the arithmetic series, which is 5.
Step 2: Identify the last term (a_n) of the arithmetic series, which is 45.
Step 3: Identify the number of terms (n) in the series, which is 10.
Step 4: Use the formula for the nth term of an arithmetic series: a_n = a + (n-1)d.
Step 5: Substitute the known values into the formula: 45 = 5 + (10-1)d.
Step 6: Simplify the equation: 45 = 5 + 9d.
Step 7: Subtract 5 from both sides: 40 = 9d.
Step 8: Divide both sides by 9 to find d: d = 40 / 9.
Step 9: Calculate the value: d = 4.44 (approximately).