In an arithmetic progression, if the sum of the first 10 terms is 250, what is t

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Question: In an arithmetic progression, if the sum of the first 10 terms is 250, what is the first term if the common difference is 5?

Options:

Correct Answer: 20

Solution:

Using the formula S_n = n/2 * (2a + (n-1)d), we can substitute n = 10 and d = 5 to find a = 20.

In an arithmetic progression, if the sum of the first 10 terms is 250, what is the first term if the common difference is 5?

In an arithmetic progression, if the sum of the first 10 terms is 250, what is the first term if the common difference is 5?

Step 1: Understand the formula for the sum of the first n terms of an arithmetic progression: S_n = n/2 * (2a + (n-1)d).
Step 2: Identify the values given in the problem: S_n = 250 (the sum of the first 10 terms), n = 10 (the number of terms), and d = 5 (the common difference).
Step 3: Substitute the known values into the formula: 250 = 10/2 * (2a + (10-1) * 5).
Step 4: Simplify the equation: 250 = 5 * (2a + 9 * 5).
Step 5: Calculate 9 * 5 = 45, so the equation becomes: 250 = 5 * (2a + 45).
Step 6: Divide both sides by 5: 50 = 2a + 45.
Step 7: Subtract 45 from both sides: 50 - 45 = 2a, which simplifies to 5 = 2a.
Step 8: Divide both sides by 2 to find a: a = 5 / 2 = 2.5.

Arithmetic Progression – A sequence of numbers in which the difference between consecutive terms is constant.
Sum of Terms Formula – The formula S_n = n/2 * (2a + (n-1)d) is used to calculate the sum of the first n terms of an arithmetic progression.