If the 5th term of an AP is 22 and d = 6, what is the 8th term?
Answer and explanation
Correct answer: 40
The relevant concept is that terms of an arithmetic progression change by the same common difference d. From the 5th term to the 8th term there are 8 - 5 = 3 steps. Each step increases the value by 6, so the total increase is 3 × 6 = 18. Starting with a_5 = 22, we obtain a_8 = 22 + 18 = 40. Therefore option D is correct. The general formula gives the same result: a_8 = a_5 + (8 - 5)d. Options A, B, and C correspond to using too few increments or an incorrect gap between the term numbers. There is no need to find the first term because a known term can be shifted directly using the common difference.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
The relevant concept is that terms of an arithmetic progression change by the same common difference d. From the 5th term to the 8th term there are 8 - 5 = 3 steps. Each step increases the value by 6, so the total increase is 3 × 6 = 18. Starting with a_5 = 22, we obtain a_8 = 22 + 18 = 40. Therefore option D is correct. The general formula gives the same result: a_8 = a_5 + (8 - 5)d. Options A, B, and C correspond to using too few increments or an incorrect gap between the term numbers. There is no need to find the first term because a known term can be shifted directly using the common difference.
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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