In (5, 12, 19, 26, ...), what are the difference of the first two terms and the difference of the third and fourth terms?
Answer and explanation
Correct answer: 7 and 7
The relevant concept is the common difference of an arithmetic progression. Compute each requested difference directly: the difference of the first two terms is 12 - 5 = 7, while the difference of the third and fourth terms is 26 - 19 = 7. Since both results are equal, the sequence is consistent with an arithmetic progression having d = 7. Option A reports both calculated differences. Option B incorrectly uses 5, which is the first term rather than a difference; option C lists terms instead of subtracting them; and option D doubles the second difference without justification. Hence option A is correct.
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What is the correct answer to this question?
7 and 7
Why is this the correct answer?
The relevant concept is the common difference of an arithmetic progression. Compute each requested difference directly: the difference of the first two terms is 12 - 5 = 7, while the difference of the third and fourth terms is 26 - 19 = 7. Since both results are equal, the sequence is consistent with an arithmetic progression having d = 7. Option A reports both calculated differences. Option B incorrectly uses 5, which is the first term rather than a difference; option C lists terms instead of subtracting them; and option D doubles the second difference without justification. Hence option A is correct.
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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