If 2, x, y, 20 are consecutive terms of an arithmetic progression, what is x + y?
Answer and explanation
Correct answer: 22
In an arithmetic progression, the difference between every pair of consecutive terms is constant. The four terms 2, x, y, 20 contain three equal gaps. The total change from the first to the last term is 20 − 2 = 18, so each common difference is d = 18/3 = 6. Therefore x = 2 + 6 = 8 and y = 8 + 6 = 14. Their sum is x + y = 8 + 14 = 22. Equivalently, the terms are 2, 8, 14, 20, which clearly have equal successive differences. Thus option C is correct; the other choices result from using an incorrect gap or adding the wrong terms.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
In an arithmetic progression, the difference between every pair of consecutive terms is constant. The four terms 2, x, y, 20 contain three equal gaps. The total change from the first to the last term is 20 − 2 = 18, so each common difference is d = 18/3 = 6. Therefore x = 2 + 6 = 8 and y = 8 + 6 = 14. Their sum is x + y = 8 + 14 = 22. Equivalently, the terms are 2, 8, 14, 20, which clearly have equal successive differences. Thus option C is correct; the other choices result from using an incorrect gap or adding the wrong 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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