In an arithmetic progression, if the sum of the first 5 terms is 50 and the firs

In an arithmetic progression, if the sum of the first 5 terms is 50 and the first term is 5, what is the common difference?

In an arithmetic progression, if the sum of the first 5 terms is 50 and the first term is 5, what is the common difference?

Step 1: Identify the given information. The first term (a) is 5, the number of terms (n) is 5, and the sum of the first 5 terms (S_n) is 50.
Step 2: Write down the formula for the sum of the first n terms of an arithmetic progression: S_n = n/2 * (2a + (n-1)d).
Step 3: Substitute the known values into the formula: 50 = 5/2 * (2*5 + (5-1)d).
Step 4: Simplify the equation: 50 = 5/2 * (10 + 4d).
Step 5: Multiply both sides by 2 to eliminate the fraction: 100 = 5 * (10 + 4d).
Step 6: Divide both sides by 5: 20 = 10 + 4d.
Step 7: Subtract 10 from both sides: 10 = 4d.
Step 8: Divide both sides by 4 to find d: d = 10 / 4.
Step 9: Simplify the result: d = 2.5.

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