In the AP (56,73,90,\ldots), how many terms are less than (1500)?
Answer and explanation
Correct answer: 85
Here, the first term is 56 and the common difference is 17. Therefore, \(a_n=56+17(n-1)\). Using \(a_n<1500\), we get \(56+17(n-1)<1500\), so \(n-1<84.94\ldots\). Hence, the greatest integer value of n is 85. In fact, \(a_{85}=1484\), whereas \(a_{86}=1501\), which is not less than 1500. Exam tip: For “less than,” do not include a term equal to the limiting value.
Frequently asked questions
What is the correct answer to this question?
85
Why is this the correct answer?
Here, the first term is 56 and the common difference is 17. Therefore, \(a_n=56+17(n-1)\). Using \(a_n<1500\), we get \(56+17(n-1)<1500\), so \(n-1<84.94\ldots\). Hence, the greatest integer value of n is 85. In fact, \(a_{85}=1484\), whereas \(a_{86}=1501\), which is not less than 1500. Exam tip: For “less than,” do not include a term equal to the limiting value.
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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