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

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Question: If the sum of the first 5 terms of an arithmetic progression is 50, what is the average of these terms? (2023)

Options:

Correct Answer: 10

Exam Year: 2023

Solution:

The average of the first n terms is given by S_n/n. Here, S_5 = 50, so the average = 50/5 = 10.

If the sum of the first 5 terms of an arithmetic progression is 50, what is the average of these terms? (2023)

If the sum of the first 5 terms of an arithmetic progression is 50, what is the average of these terms? (2023)

Step 1: Understand that an arithmetic progression (AP) is a sequence of numbers where the difference between consecutive terms is constant.
Step 2: Know that the sum of the first n terms of an AP is denoted as S_n.
Step 3: In this question, we are given that the sum of the first 5 terms (S_5) is 50.
Step 4: The average of the first n terms is calculated using the formula: Average = S_n / n.
Step 5: Here, n is 5, so we will use the formula: Average = S_5 / 5.
Step 6: Substitute the value of S_5 into the formula: Average = 50 / 5.
Step 7: Calculate the average: 50 divided by 5 equals 10.
Step 8: Conclude that the average of the first 5 terms of the arithmetic progression is 10.

Arithmetic Progression – A sequence of numbers in which the difference between consecutive terms is constant.
Sum of Terms – The total value obtained by adding a specified number of terms in a sequence.
Average Calculation – The average is calculated by dividing the sum of values by the number of values.