If a_4 = 18 and d = 3, what is the 9th term?
Answer and explanation
Correct answer: 33
The governing property is the constant difference between consecutive terms of an arithmetic progression. The 9th term is 9 - 4 = 5 positions after the 4th term. Since every position increases by d = 3, the total increase is 5 × 3 = 15. Using the known term directly, a_9 = a_4 + (9 - 4)d = 18 + 5 × 3 = 33. Hence option D is correct. This method avoids unnecessarily calculating the first term. Option A is obtained by taking only four increments, while options B and C do not result from adding five equal differences of 3 to 18. The direction is forward because the requested index 9 is greater than the given index 4.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
The governing property is the constant difference between consecutive terms of an arithmetic progression. The 9th term is 9 - 4 = 5 positions after the 4th term. Since every position increases by d = 3, the total increase is 5 × 3 = 15. Using the known term directly, a_9 = a_4 + (9 - 4)d = 18 + 5 × 3 = 33. Hence option D is correct. This method avoids unnecessarily calculating the first term. Option A is obtained by taking only four increments, while options B and C do not result from adding five equal differences of 3 to 18. The direction is forward because the requested index 9 is greater than the given index 4.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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