Question

The 6th term of an AP is 1 more than twice its 8th term if the 12th term of the AP is 47 then find n th term.​

Answer 1

Answer:

Let us assume that a and d are first term and common difference of the AP respectively.

Given that the 6th term of an AP is 1 more than twice the 8th term.

lt give one equation in the form of a and d .

and also given that 12th term of that ap is 47 which give second equation in a and d .

After solving these two equations simultaneously we will get the values of a and d respectively .

After then we will put those values of a and d in the formula of calculating and its term of an AP as shown in attachment .

Answer 2

$\tt\huge{Solution:}$

a6 = a + 5d

a8 = a + 7d

Now,

a + 5 d = 2 ( a+7d) + 1

=> a + 5d =( 2a + 14 d) + 1

=> a + 9 d = -1

a12 = a + 11d = 47

a = - 217

d = 24

$\tt\huge{According \:to \:question}$

an = a + (n-1)d

= -217 + (n -1)24

= -217 + 24n - 24

$\huge{24n - 241}$