If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be ______.

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If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be 0. Explanation: According to the question, 7a7 = 11a11 $\Rightarrow$ 7[a + (7 – 1)d] = 11[a + (11 – 1)d] ...[∵ an = a + (n – 1)d] $\Rightarrow$ 7(a + 6d) = 11(a + 10d) $\Rightarrow$ 7a + 42d = 11a + 110d $\Rightarrow$ 4a + 68d = 0 $\Rightarrow$ 2(2a + 34d) = 0 $\Rightarrow$ 2a + 34d = 0 ...[∵ 2 $\neq$ 0] $\Rightarrow$ a + 17d = 0 ...(i) $\therefore$ 18th term of an AP, a18 = a + (18 – 1)d = a + 17d = 0 ...[From equation (i)]

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