If the (25)th term of the AP (t-8,t-1,t+6,\ldots) is (230), what is the value of (t)?
Answer and explanation
Correct answer: 70
The difference between consecutive terms is \(7\), so the first term is \(a=t-8\) and the common difference is \(d=7\). The \(25\)th term is \(a_{25}=a+24d\). Thus, \(230=(t-8)+24\times7=t+160\), giving \(t=70\). If \(t=66\), the \(25\)th term would be \(226\), so it is not correct. Exam tip: in the formula for the \(n\)th term, multiply \(d\) by \(n-1\), not by \(n\).
Frequently asked questions
What is the correct answer to this question?
70
Why is this the correct answer?
The difference between consecutive terms is \(7\), so the first term is \(a=t-8\) and the common difference is \(d=7\). The \(25\)th term is \(a_{25}=a+24d\). Thus, \(230=(t-8)+24\times7=t+160\), giving \(t=70\). If \(t=66\), the \(25\)th term would be \(226\), so it is not correct. Exam tip: in the formula for the \(n\)th term, multiply \(d\) by \(n-1\), not by \(n\).
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.
