Question

The 6th term of ap is 1 more than twice its 8th term if 12th term of the ap is47then find its nth term

Answer 1

Hi there,

I think the question has some incorrect data because 6th term of A.P cannot be more than its 8th term. Hoping the correct question to be as follows and solving it accordingly:

The 16th term of A.P. is 1 more than twice its 8th term if 12th term of the A.P. is 47. Then find its nth term?

Answer: nth term = (4n - 1)

Explanation:

We are given that,

a₁₆ = 1 + (2 * a₈)

⇒  a + 15d = 1 + 2(a+7d)

⇒ a + 15d = 1 + 2a + 14d

⇒ a = d - 1 …….. (i)

Also given,

a₁₂ = 47

⇒ a + 11d = 47  

substituting value of a from (i), we get

⇒ d - 1 + 11d = 47

⇒ 12d = 48

⇒ d = 4  .... (ii)

Now, substituting the value of d in (i), we get

a = 4 -1 = 3  ... (iii)

Thus,

The nth term of the A.P. is given as,

= a + (n - 1)d

= 3 + (n - 1)4 ….. [∵ from (ii) & (iii), a = 3 & d = 4]

= 3 + 4n - 4

= 4n - 1

Hope this is helpful!!!!!