The AP of multiples of (17) greater than (500) is (510,527,544,\ldots). What is its (19)th term?
Answer and explanation
Correct answer: 816
The first term is \(a=510\), and the common difference is \(d=527-510=17\). The \(n\)th term of an AP is \(a_n=a+(n-1)d\). Therefore, \(a_{19}=510+(19-1)\times17=510+306=816\). Hence, 816 is correct. The value 833 results from incorrectly counting 20 differences instead of the 18 differences from the first term to the 19th term. Exam tip: always use \((n-1)\), not \(n\), in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
816
Why is this the correct answer?
The first term is \(a=510\), and the common difference is \(d=527-510=17\). The \(n\)th term of an AP is \(a_n=a+(n-1)d\). Therefore, \(a_{19}=510+(19-1)\times17=510+306=816\). Hence, 816 is correct. The value 833 results from incorrectly counting 20 differences instead of the 18 differences from the first term to the 19th term. Exam tip: always use \((n-1)\), not \(n\), in the nth-term formula.
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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