Mathematics
Finding the $n$th term of an AP
Practice questions
If (a_n=8n+q) and (a_{6n}-a_{2n}=384), what is the value of (n)?Which of the following formulas defines an arithmetic progression (AP)?If (a_{2n+1}=89), (a_{n+1}=41), and (d=6), what is (n)?If an arithmetic progression has first term 7 and common difference 5, which of the following expressions correctly represents its nth term?The first row of an auditorium has 24 seats, and each succeeding row has 4 more seats. A student says that the row with 100 seats is the 19th row because they used \(24+4n=100\). After correcting the student's error, which is the correct row?If (a_n=7n+c) and (a_6=61), what is (r) when (a_{4r}=299)?If an arithmetic progression satisfies \(a_m=a_n\) for \(m\ne n\), which statement must be true?Which of the following relations is always true for an arithmetic progression, where \(r\) is a positive integer and all indices are valid?In an AP, (a_8=46) and (a_{22}=144). What is the value of (a_{40})?If (a_{3m}=152), (a_m=56), and (d=8), what is the value of (m)?If (a_n=kn+17) and (a_{20}-a_7=104), what is (a_{31})?Which of the following nth-term formulas defines an arithmetic progression (AP) necessarily?The \(n\)th term of a sequence is \(a_n=4n-7\). What is the most appropriate reason for identifying it as an arithmetic progression (AP)?In an AP, (a_{12}=3a_5+4) and (a_5=19). What is (a_{26})?Which of the following rules defines the nth term of an arithmetic progression for every positive integer n?If (a_n=9n+c) and (a_8=101), what is (r) when (a_{5r}=326)?What is the first term greater than (850) in the AP (27,40,53,\ldots)?Which of the following sequences has the same difference between every pair of consecutive terms and is therefore an arithmetic progression (AP)?If the \(p\)th term of an AP is \(a_p\) and its common difference is \(d\), which relation correctly gives the \(n\)th term?Which of the following nth-term rules represents an AP?