Question

If 7 times the 7th term of an AP is equal to 11 times the 11th term, then its 18th term will be
(a) 7
(b) 11
(c) 18
(d) 0

Answer 1

( d) 0
In the given AP, let the first term be a and the common difference be d.
We have T_n = a + (n - 1)d
​Then T₇ = a + (7 - 1)d = a + 6d

Also, T₁₁ = a + (11 - 1)d = a + 10d

Now, (7 ⨯ T₇) = (11 ⨯ T₁₁)
⇒ 7[ a + 6d] = 11[a + 10d]
⇒ 7a + 42d = 11a + 110 d

⇒ 4a = -68d
⇒ a = -17d

∴ T₁₈ = a + (18 - 1)d =​ a + 17d = -17d + 17d = 0 [ ∵ a = - 17d]​
​Hence, the 18^th term is 0 (zero).