Question

If 4 times the 4th term of AP is equal to 7 times the 7th term. proof that 11th term is 0
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Answer 1

Answer:

We know, t

n

=a+(n−1)d

Then t

7

=a+(7−1)d

⇒t

7

=a+6d

and t

11

=a+(11−1)d

⇒t

11

=a+10d

Given that 7t

7

=11t

11

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

⇒7a+42d=11a+110d

⇒11a+110d−7a−42d=0

⇒4a+68d=0

⇒a+17d=0

⇒a+(18−1)d=0

⇒t

18

=0

Impossible to find first term and common difference.

Since these two are unknown but one equation is given