What is the first term greater than (500) in the AP (17,27,37,\ldots)?
Answer and explanation
Correct answer: 507
Here, the first term is 17 and the common difference is 10. Thus, \(a_n=17+10(n-1)=10n+7\). From \(10n+7>500\), we get \(n>49.3\), so the least integer value of \(n\) is 50. Therefore, \(a_{50}=507\), which is the first term greater than 500. The close distractor 497 is the preceding term, since \(a_{49}=497\). Exam tip: For “greater than”, use the next integer value after solving the inequality.
Frequently asked questions
What is the correct answer to this question?
507
Why is this the correct answer?
Here, the first term is 17 and the common difference is 10. Thus, \(a_n=17+10(n-1)=10n+7\). From \(10n+7>500\), we get \(n>49.3\), so the least integer value of \(n\) is 50. Therefore, \(a_{50}=507\), which is the first term greater than 500. The close distractor 497 is the preceding term, since \(a_{49}=497\). Exam tip: For “greater than”, use the next integer value after solving the inequality.
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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