If (4, k, 14, 19, …) is an arithmetic progression, what is the value of k?
Answer and explanation
Correct answer: 9
In an arithmetic progression, the difference between every pair of consecutive terms is constant. The difference from 14 to 19 is 19 − 14 = 5, so the common difference is d = 5. Moving one step backward from 14 gives k = 14 − 5 = 9. This also checks with the beginning: k − 4 = 9 − 4 = 5. Thus the sequence is 4, 9, 14, 19, … and option D is correct. The other choices fail the equal-difference condition: they would not make both k − 4 and 14 − k equal to 5.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
In an arithmetic progression, the difference between every pair of consecutive terms is constant. The difference from 14 to 19 is 19 − 14 = 5, so the common difference is d = 5. Moving one step backward from 14 gives k = 14 − 5 = 9. This also checks with the beginning: k − 4 = 9 − 4 = 5. Thus the sequence is 4, 9, 14, 19, … and option D is correct. The other choices fail the equal-difference condition: they would not make both k − 4 and 14 − k equal to 5.
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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