If (a_n=100-7n), which is the first term less than (30)?
Answer and explanation
Correct answer: 11th term
Given \(a_n=100-7n\), a term smaller than 30 must satisfy \(100-7n<30\). This gives \(-7n<-70\), so \(n>10\). The smallest natural-number value of \(n\) is 11; therefore, the 11th term is the first term less than 30. The 10th term is \(a_{10}=30\), which is not less than 30. Exam tip: for “less than,” use \(<\); an equal value is not included.
Frequently asked questions
What is the correct answer to this question?
11th term
Why is this the correct answer?
Given \(a_n=100-7n\), a term smaller than 30 must satisfy \(100-7n<30\). This gives \(-7n<-70\), so \(n>10\). The smallest natural-number value of \(n\) is 11; therefore, the 11th term is the first term less than 30. The 10th term is \(a_{10}=30\), which is not less than 30. Exam tip: for “less than,” use \(<\); an equal value is not included.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
