If 7 times the 7th term of an AP is equal to 11 times its 11th term , then its 18th term will be

If 7 times the 7th term of an AP is equal to 11 times its 11th term ,

1.	If 7 times the 7th term of an AP is equal to 11 times its 11th term , then its 18th term will be
Answer» let a = first term and d=common difference.According to question,7a7\xa0= 11 a11=>7(a+6d) = 11(a+10d)=> 7a-11a = 110d-42d=> -4a = 68d=>a = -17d ......(1)Now , a18\xa0= a\xa0+17d\xa0but a = -17 d ..by (1)so\xa0put this\xa0value , we get,a18=-17d +17d =0\xa0Hence proved.