Q. 174.8( 10 Votes )
If 7 times the 7th term of an AP is equal to 11 times its 11th term, show that the 18th term of the AP is zero.
Answer :
Show that: 18th term of the AP is zero.
Given: 7a7= 11a11
(Where a7 is Seventh term, a11 is Eleventh term, an is nth term and d is common difference of given AP)
Formula Used: an = a + (n - 1)d
7(a + 6d) = 11(a + 10d)
7a + 42d = 11a + 110d 
68d = (–4a)
a + 17d= 0 ….equation (i)
Now a18 = a + (18 - 1)d
So a + 17d = 0 [by using equation (i)]
HENCE PROVED
[NOTE: If n times the nth term of AP is equal to m times the mth term of same AP then its (m + n)th term is equal to zero]
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