# If 7 times the 7th term of an AP is equal to 11 times the 11th term, show that the 18th term of it is 0

2
by chroopa

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by chroopa

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(a+6d)7 since 7th term of the ap is 7 times and the same for 11th term

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

7a + 42d =11a +110d (on solving)

7a - 11a = 110d - 42d

-4a = -68d

a= -17d

we know 18th term = (a+17d)................................. (i)

now we substitute the value of a in (i)

which emplies,

-17d + 17d

= 0

hence prove..

We have to prove that that a+17d = 0

Now,

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

7a+42d = 11a+110d

4a+68d = 0

4(a+17d) = 0

a+17d = 0

Hence proved.