If (12, b, 2b-3, 39) are in an arithmetic progression, what is the value of (b)?
Answer and explanation
Correct answer: (21)
In an arithmetic progression, the difference between every pair of consecutive terms is the same. Here the four terms are 12, b, 2b−3, and 39. Because there are four terms, the change from the first term to the fourth term contains three equal common differences. This lets us determine the common difference before finding b.
The total change is 39−12=27. Therefore, the common difference is \(d=27/3=9\). The second term is one common difference after the first, so \(b=12+9=21\). Checking the next term gives \(2b−3=2(21)−3=39\), which is consistent with the fourth term. Thus option C, 21, is correct. A value such as 20 would not produce equal consecutive differences.
Frequently asked questions
What is the correct answer to this question?
(21)
Why is this the correct answer?
In an arithmetic progression, the difference between every pair of consecutive terms is the same. Here the four terms are 12, b, 2b−3, and 39. Because there are four terms, the change from the first term to the fourth term contains three equal common differences. This lets us determine the common difference before finding b.
The total change is 39−12=27. Therefore, the common difference is \(d=27/3=9\). The second term is one common difference after the first, so \(b=12+9=21\). Checking the next term gives \(2b−3=2(21)−3=39\), which is consistent with the fourth term. Thus option C, 21, is correct. A value such as 20 would not produce equal consecutive differences.
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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