determine the 2nd term and rth term of AP.whow 6th term 12 and 8th ter

1.	determine the 2nd term and rth term of AP.whow 6th term 12 and 8th term is 22.
Answer» Given a6\xa0= 12{tex}\\Rightarrow{/tex}\xa0a + (6 - 1)d = 12{tex}\\Rightarrow{/tex}\xa0a + 5d = 12 ............(i)and, a8\xa0= 22{tex}\\Rightarrow{/tex}\xa0a + (8\xa0- 1)d = 22{tex}\\Rightarrow{/tex}\xa0a + 7d = 22 ............(ii)Subtracting equation (i) from (ii), we get(a + 7d) - (a + 5d ) = 22 - 12{tex}\\Rightarrow{/tex}\xa0a + 7d - a - 5d = 10{tex}\\Rightarrow{/tex}2d - 10{tex}\\Rightarrow \\quad d = \\frac { 10 } { 2 } = 5{/tex}Using value of d in equation (i), we geta + 5\xa0{tex}\\times{/tex}\xa05 = 12{tex}\\Rightarrow{/tex}\xa0a = 12 - 25 = -13nth term(an) = a + (n - 1)a= -13 + (n - 1)(5)= 5n - 18

Discussion