If 7 times the seventh term of an Arithmetic Progression (AP) is equal to 11 times its eleventh term, then the 18th term of the AP will be

Answer: Option A

Let the first term of the AP be a and the common difference = d
7^th term = A₇ = a + 6d
11^th term = A₁₁ = a + 10d
According to question,
⇒ 7 × (a + 6d) = 11 × (a + 10d)
⇒ 7a + 42d = 11a + 110d
⇒ 11a - 7a = 42d - 110d
⇒ 4a = -68d
⇒ a = -17d
⇒ a + 17d = 0 = A₁₈