Question 8 (OR 2nd question)
If 7 times the 7th term of an A.P is equal to 11 times its 11th term, then find its 18th term.
We know that
an = a + (n – 1)d
Given that
7 times the 7th term is equal to 11 times its 11th term
7 × a7 = 11 × a11
7 × (a + (7 – 1)d) = 11 × (a + (11 – 1)d)
7 × (a + 6d) = 11 × (a + 10d)
7a + 42d = 11a + 110d
7a – 11a = 110d – 42d
–4a = 68d
a = 68𝑑/(−4)
a = –17d
Now, we need to find the 18th term
a18 = a + (18 – 1)d
= a + 17d
Putting a = –17d
= –17d + 17d
= 0
So, 18th term is 0

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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