What is the 15th term of the AP (1, 4, 7, 10, ...)?
Answer and explanation
Correct answer: 43
The governing rule for the nth term of an arithmetic progression is a_n = a + (n − 1)d. In the given AP, the first term is a = 1 and the common difference is d = 4 − 1 = 3. The 15th term is reached after 15 − 1 = 14 equal jumps from the first term. Hence a_15 = 1 + 14 × 3 = 1 + 42 = 43. Therefore option C is correct. Option B is only 14 × 3 and leaves out the initial term. Option D results from adding one extra difference, as if fifteen jumps were needed. Option A does not satisfy the sequence rule, since the terms increase by 3 each time. Remembering that the number of jumps is one less than the term number prevents the common off-by-one error.
Frequently asked questions
What is the correct answer to this question?
43
Why is this the correct answer?
The governing rule for the nth term of an arithmetic progression is a_n = a + (n − 1)d. In the given AP, the first term is a = 1 and the common difference is d = 4 − 1 = 3. The 15th term is reached after 15 − 1 = 14 equal jumps from the first term. Hence a_15 = 1 + 14 × 3 = 1 + 42 = 43. Therefore option C is correct. Option B is only 14 × 3 and leaves out the initial term. Option D results from adding one extra difference, as if fifteen jumps were needed. Option A does not satisfy the sequence rule, since the terms increase by 3 each time. Remembering that the number of jumps is one less than the term number prevents the common off-by-one error.
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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