What is the 9th term of the AP 11, 16, 21, 26, ...?
Answer and explanation
Correct answer: 51
The relevant rule is aₙ = a + (n − 1)d for the nth term of an AP. The first term is a = 11, and the common difference is d = 16 − 11 = 5. For n = 9, a₉ = 11 + (9 − 1)×5 = 11 + 8×5 = 11 + 40 = 51. Therefore option D is correct. Only eight differences are added because the first term is already term one; moving from term one to term nine requires eight steps. Option A stops too early, option B uses an incorrect number of increments, and option C adds two extra steps. The sequence 11, 16, 21, ..., 51 also confirms the calculation.
Frequently asked questions
What is the correct answer to this question?
51
Why is this the correct answer?
The relevant rule is aₙ = a + (n − 1)d for the nth term of an AP. The first term is a = 11, and the common difference is d = 16 − 11 = 5. For n = 9, a₉ = 11 + (9 − 1)×5 = 11 + 8×5 = 11 + 40 = 51. Therefore option D is correct. Only eight differences are added because the first term is already term one; moving from term one to term nine requires eight steps. Option A stops too early, option B uses an incorrect number of increments, and option C adds two extra steps. The sequence 11, 16, 21, ..., 51 also confirms the calculation.
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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