If a, b, c are in AP and a + b + c = 27, what is the middle term b?
Answer and explanation
Correct answer: 9
For three consecutive terms of an arithmetic progression, the middle term is the arithmetic mean of the other two, so a + c = 2b. Equivalently, the three terms can be written as b − d, b, and b + d. Their sum is (b − d) + b + (b + d) = 3b because the −d and +d cancel. Given a + b + c = 27, we obtain 3b = 27, hence b = 9. Therefore option C is correct. The values 7, 8, and 10 do not satisfy the required sum relation b = 27/3; the answer does not depend on knowing a or c separately.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
For three consecutive terms of an arithmetic progression, the middle term is the arithmetic mean of the other two, so a + c = 2b. Equivalently, the three terms can be written as b − d, b, and b + d. Their sum is (b − d) + b + (b + d) = 3b because the −d and +d cancel. Given a + b + c = 27, we obtain 3b = 27, hence b = 9. Therefore option C is correct. The values 7, 8, and 10 do not satisfy the required sum relation b = 27/3; the answer does not depend on knowing a or c separately.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..
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