If the fourth term of the arithmetic progression (x, x + 8, x + 16, …) is 41, what is x?
Answer and explanation
Correct answer: 17
The sequence has first term x and common difference 8. The fourth term is obtained after three equal increments, so a₄ = x + 3 × 8 = x + 24. Since a₄ is given as 41, solve x + 24 = 41, which gives x = 41 − 24 = 17. Therefore, option B is correct. A direct check confirms the result: the terms become 17, 25, 33, 41. Option A would produce a fourth term of 39, option C would produce 43, and option D would produce 45. The important concept is that the first term itself is x, so only three common differences are added to reach the fourth term, not four.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
The sequence has first term x and common difference 8. The fourth term is obtained after three equal increments, so a₄ = x + 3 × 8 = x + 24. Since a₄ is given as 41, solve x + 24 = 41, which gives x = 41 − 24 = 17. Therefore, option B is correct. A direct check confirms the result: the terms become 17, 25, 33, 41. Option A would produce a fourth term of 39, option C would produce 43, and option D would produce 45. The important concept is that the first term itself is x, so only three common differences are added to reach the fourth term, not four.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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