If 7 times the seventh term of an Arithmetic Progression

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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

1. 1
2. 0
3. 2
4. –1

Correct Option: B

We know that , nth term of an arithmetic progression = a_n = a + (n – 1) d
Here , n = 7 and 11
∴ a₇ = a + (7 – 1) d = a + 6d
a₁₁ = a + (11 – 1) d = a + 10d
According to the question,
7 a₇ = 11 a₁₁
⇒ 7 (a + 6d) = 11 (a + 10d)
⇒ 7a + 42d = 11a + 110 d
⇒ 11a – 7a = 42d – 110d
⇒ 4a = – 68d
⇒ a = – 17d .... (i)
∴ a₁₈ = a + (18 – 1)d = a + 17d = –17d + 17d = 0