Question

If 7 times the 7th term of an A.P. is equal to 11 times the 11th term,show that 18th term of A.P. is 0.​

Answer 1

7A7 = 11 A11

7(a+ 6d ) =11(a+ 10d)

7a + 42d = 11a + 110d

4a + 68d= 0

4(a+ 17d)= 0

a+ 17d =0

hence A18 = 0 PROVED

Answer 2

let the first term. be a

and common difference be d

given

7*term7 = 11*term11

=>7(a+6d) = 11(a+10d)

=>7a + 42d = 11a + 110d

=>4a +68d=0

=>4(a+17d)=0

=>a + 17d =0

=>a + (18-1)d = 0

but

term 18 = a +(17-1)d

so 18th term =0