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

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Question: In an arithmetic progression, if the sum of the first 5 terms is 50, what is the first term if the common difference is 2?

Options:

Correct Answer: 10

Solution:

Using the sum formula S_n = n/2 * (2a + (n-1)d), we have 50 = 5/2 * (2a + 8). Solving gives a = 10.

In an arithmetic progression, if the sum of the first 5 terms is 50, what is the first term if the common difference is 2?

In an arithmetic progression, if the sum of the first 5 terms is 50, what is the first term if the common difference is 2?

Step 1: Identify the formula for the sum of the first n terms of an arithmetic progression: S_n = n/2 * (2a + (n-1)d).
Step 2: Substitute the known values into the formula. Here, n = 5 (the number of terms), S_n = 50 (the sum), and d = 2 (the common difference).
Step 3: Plug in the values: 50 = 5/2 * (2a + (5-1)*2).
Step 4: Simplify the equation: 50 = 5/2 * (2a + 8).
Step 5: Multiply both sides by 2 to eliminate the fraction: 100 = 5 * (2a + 8).
Step 6: Divide both sides by 5: 20 = 2a + 8.
Step 7: Subtract 8 from both sides: 20 - 8 = 2a, which simplifies to 12 = 2a.
Step 8: Divide both sides by 2 to solve for a: a = 12 / 2, which gives a = 6.

Arithmetic Progression – Understanding the properties and formulas related to arithmetic sequences, particularly the sum of terms.
Sum of Terms Formula – Application of the formula S_n = n/2 * (2a + (n-1)d) to find the sum of a specified number of terms in an arithmetic progression.
Algebraic Manipulation – Skills in rearranging and solving equations to isolate variables.