If 13, b, 31 are consecutive terms of an arithmetic progression, what is b?
Answer and explanation
Correct answer: 22
In three consecutive terms of an arithmetic progression, the middle term is the arithmetic mean of the first and third terms. Therefore b = (13 + 31)/2 = 44/2 = 22. Equivalently, equal successive differences require b − 13 = 31 − b; solving gives 2b = 44 and b = 22. Hence option C is correct. With b = 22, both differences are 9: 22 − 13 = 9 and 31 − 22 = 9. The other options do not make the two consecutive differences equal; for example, b = 18 gives differences 5 and 13. The middle-term average rule applies because the three values are consecutive AP terms.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
In three consecutive terms of an arithmetic progression, the middle term is the arithmetic mean of the first and third terms. Therefore b = (13 + 31)/2 = 44/2 = 22. Equivalently, equal successive differences require b − 13 = 31 − b; solving gives 2b = 44 and b = 22. Hence option C is correct. With b = 22, both differences are 9: 22 − 13 = 9 and 31 − 22 = 9. The other options do not make the two consecutive differences equal; for example, b = 18 gives differences 5 and 13. The middle-term average rule applies because the three values are consecutive AP terms.
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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