Mathematics
Finding the $n$th term of an AP
Practice questions
In an AP, (a_{10}=0) and (a_{21}=-55). What is (a_1)?Which of the following sequences does not have its nth term forming an arithmetic progression (AP)?In the AP (97,88,79,\ldots), what is the first term less than (20)?The terms of a sequence are denoted by \(a_n\). Which of the following conditions, if true for every \(n\), guarantees that the sequence is an arithmetic progression?In an AP, \(a_3=11\) and \(a_{13}=51\). If \(a_{3r}=91\), what is (r)?If in an AP (a_2=2x+1), (a_5=5x-2), and (a_8=8x-5), what is (a_{11})?In the AP (14,23,32,\ldots), what is the greatest term between (300) and (350)?If \(a_{n+2}-a_n=18\) and \(a_9=74\), what is \(a_{25}\)?In an AP, (a_1+a_4=38) and (a_7=44). What is (a_{16})?If \(a_6=2a_3+5\) and \(a_3=13\), what is \(a_{12}\)?What is the (18)th term of the AP \(-7,\frac{-3}{2},4,\ldots\)?If \(a_{20}=3a_8\) and \(a_8=28\), what is \(a_{26}\)?In an AP, (a_{15}=a_5+50) and (a_5=24). What is (a_{31})?If \(a_n=an+b\), \(a_4=21\), and \(a_{14}=71\), what is \(a_{30}\)?In the AP (64,57,50,\ldots), which is the last term greater than (-20)?In an elevator test, the first cycle has (240) kg load and (15) kg is reduced in each next cycle. In which cycle will the load be (75) kg?A student solves (18) questions on the first day and (4) more questions each day. On which day will he solve (102) questions?If \(a_1=3\), \(a_{2n+1}=123\), and \(d=4\), what is the value of (n)?In an AP, (a_{3n}=81), (a_n=21), and (d=5). What is (n)?If \(a_{12}=5a_4-8\) and \(a_4=17\), what is \(a_{20}\)?