Question

If 7th term of an Arithmetic Progression is equal to 11 times the eleventh term,show that the 18th tern of the A.P. is zero.

Answer 1

This is a wrong question. The right one is :
If 7 times of the 7th term of an Arithmetic Progression is equal to 11 times the eleventh term,show that the 18th tern of the A.P. is zero.
Let a is the first term and d is the common factor of the A.P. Then,
7[a+(7-1)d]=11[a+(11-1)d]
or, 7(a+6d)=11(a+10d)
or, 7a+42d=11a+110d
or, 7a-11a=110d-42d
or, -4a=68d
or, -4a-68d=0
or, -4(a+17d)=0
or, a+(18-1)d=0
or, t₁₈=0 (Proved)