The nth term of the AP (55, 51, 47, ...) is −17. What is n?
Answer and explanation
Correct answer: 19
Apply the nth-term formula a_n = a + (n − 1)d. The first term is a = 55 and the common difference is d = 51 − 55 = −4. Since the nth term is −17, write −17 = 55 + (n − 1)(−4). Subtracting 55 gives −72 = −4(n − 1), and dividing by −4 gives 18 = n − 1. Hence n = 19, so option C is correct. The sign of the common difference must remain negative because the AP decreases by 4. A useful check is that the 19th term is 55 − 18 × 4 = 55 − 72 = −17. Option B would give −13, while option D would give −21, confirming that only 19 works.
Frequently asked questions
What is the correct answer to this question?
19
Why is this the correct answer?
Apply the nth-term formula a_n = a + (n − 1)d. The first term is a = 55 and the common difference is d = 51 − 55 = −4. Since the nth term is −17, write −17 = 55 + (n − 1)(−4). Subtracting 55 gives −72 = −4(n − 1), and dividing by −4 gives 18 = n − 1. Hence n = 19, so option C is correct. The sign of the common difference must remain negative because the AP decreases by 4. A useful check is that the 19th term is 55 − 18 × 4 = 55 − 72 = −17. Option B would give −13, while option D would give −21, confirming that only 19 works.
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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