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Question
If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be ______.
Options
7
11
18
0
Solution
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
⇒ 7[a + (7 – 1)d] = 11[a + (11 – 1)d] ...[∵ an = a + (n – 1)d]
⇒ 7(a + 6d) = 11(a + 10d)
⇒ 7a + 42d = 11a + 110d
⇒ 4a + 68d = 0
⇒ 2(2a + 34d) = 0
⇒ 2a + 34d = 0 ...[∵ 2 ≠ 0]
⇒ a + 17d = 0 ...(i)
∴ 18th term of an AP,
a18 = a + (18 – 1)d
= a + 17d
= 0 ...[From equation (i)]
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