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  • If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18thterm will be (A) 7 (B) 11 (C) 18 (D) 0

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

(A) 7

(B) 11

(C) 18

(D) 0

Answers (1)

\text{Given } 7 \times a_{7} = 11 \times a_{11} \\ 7 \times (a + 6d) = 11 \times (a + 10d) \quad (\text{Using } a_{n} = a + (n - 1) \times d) \\ 7a + 42d = 11a + 110d \\ 11a - 7a + 110d - 42d = 0 \\ 4a + 68d = 0 \\ \text{Dividing by } 4 \text{, we get} \\ a + 17d = 0 \quad (1) \\ a_{18} = a + (18 - 1)d \\ = a + 17d \\ = 0 \\

Hence option D is correct.

Posted by

infoexpert21

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