In the AP (5,12,19,\ldots), what is the greatest term less than (150)?
Answer and explanation
Correct answer: 145
Here, the first term is 5 and the common difference is 7. The nth term is \(a_n=5+7(n-1)=7n-2\). From \(7n-2<150\), we get \(n<\frac{152}{7}\), so the greatest integer value of \(n\) is 21. Hence, \(a_{21}=7(21)-2=145\). The numbers 146, 147, and 148 are not terms of this AP because they do not occur when starting from 5 and adding 7 each time. Exam tip: for “less than,” use a strict inequality, not equality.
Frequently asked questions
What is the correct answer to this question?
145
Why is this the correct answer?
Here, the first term is 5 and the common difference is 7. The nth term is \(a_n=5+7(n-1)=7n-2\). From \(7n-2<150\), we get \(n<\frac{152}{7}\), so the greatest integer value of \(n\) is 21. Hence, \(a_{21}=7(21)-2=145\). The numbers 146, 147, and 148 are not terms of this AP because they do not occur when starting from 5 and adding 7 each time. Exam tip: for “less than,” use a strict inequality, not equality.
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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