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.

Transcript

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
Given that
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
= 0
So, 12th term is 0

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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