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Home » 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.
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.
RS aggarwal class 11 Maths Arithmetic progressions
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.

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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