The 19th term of an AP is equal to three times its sixth term.if its 9th term is 19,find the AP

The 19th term of an AP is equal to three times its sixth term.if its 9

1.	The 19th term of an AP is equal to three times its sixth term.if its 9th term is 19,find the AP
Answer» Let a be the first term and d be the common difference of the AP. Then, a19=3(a6)a9=19a+8d=19a=19-8d .......(1) a19=3(a6)a+18d=3(a+5d)a+18d=3a+15d18d-15d=3a-a3d=2a3d=2(19-8d) ........(from 1)3d=38-16d3d+16d=3819d=38d=38/2d=2. ......(2)Put d=2 in eq.1a=19-8×2a=3now put values of a &d in above equationa19=3(a6)a+18d=3(a+5d)3+18×2=3(3+5×2)3+36=3(3+10)39=9+3039=39 .•. AP= 3,5,7......H.P.Hope this helps.?Regards