Show that: 18^th term of the AP is zero.

Given: 7a₇= 11a₁₁

(Where a₇ is Seventh term, a₁₁ is Eleventh term, a_n is nth term and d is common difference of given AP)

Formula Used: a_n = 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 n^th term of AP is equal to m times the m^th term of same AP then its (m + n)^th term is equal to zero]