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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.