Mathematics
Finding the $n$th term of an AP
Practice questions
In an AP, (a_{10}=4a_4+6) and (a_4=14). What is (a_{22})?Which of the following sequences has an nth term that represents an arithmetic progression?If (a_n=7n+c) and (a_6=61), what is (r) when (a_{4r}=313)?What is the first term greater than (700) in the AP (19,30,41,\ldots)?An arithmetic progression has an odd number of terms. The sum of its first and last terms is equal to twice which term?If the \(n\)th term of a sequence is \(a_n=7-3n\), which of the following correctly identifies this arithmetic progression?Which statement correctly classifies the sequence whose \(n\)th term is \(a_n=5-3n\)?What will be the (38)th term of the AP \(8,\frac{25}{2},17,\ldots\)?In an AP, (a_{18}=0) and (a_{42}=-192). What is (a_1)?Which of the following nth-term expressions represents an AP in which each successive term decreases by 3?In the AP (169,154,139,\ldots), what is the first term less than (40)?If in an AP (a_{27}=a_8+171), what is the common difference?In an AP, (a_7=38) and (a_{19}=122). If (a_{7r}=206), what is (r)?If in an AP (a_5=5x-2), (a_{11}=11x-20), and (a_{17}=17x-38), what is (a_{23})?In the AP (31,45,59,\ldots), what is the greatest term between (900) and (1000)?The nth term of an arithmetic progression is \(a_n=pn+q\), where \(p\) and \(q\) are constants. What is the common difference of the progression?In an AP, (a_4+a_9=95) and (a_{16}=137). What is (a_{31})?If (a_8=37) and (a_{12}=2a_8+22), what is (a_{28})?What will be the (31)st term of the AP (-13,\frac{-11}{2},2,\ldots)?Under which condition does the \(n\)th term of an arithmetic progression remain independent of the value of \(n\)?