Question 1 – Choice 2 If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.
We know that
an = a + (n – 1)d
7 times the 7th term is equal to 5 times its 5th term
7 × a7 = 5 × a5
7 × (a + (7 – 1)d) = 5 × (a + (5 – 1)d)
7 × (a + 6d) = 5 × (a + 4d)
7a + 42d = 5a + 20d
7a – 5a = 20d – 42d
2a = −22d
a = (−22𝑑)/2
a = –11d
Now, we need to find the 12th term
a12 = a + (12 – 1)d
= a + 11d
Putting a = –11d
= –11d + 11d
So, 12th term is 0
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.
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