If 7 times the 7th term of an AP is equal to 11 times its 11th term, s

1.	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: 18^th term of the AP is zero. Given: 7a₇= 11a₁₁ (Where a₇is Seventh term, a₁₁ is Eleventh term, a_n is n^th 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]

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: 18^th term of the AP is zero.

Given: 7a₇= 11a₁₁

(Where a₇is Seventh term, a₁₁ is Eleventh term, a_n is n^th 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]