Question

the 16th term of an A.P is one more than twice its 8th term. if the twelth term of the A.P is 47, then find its n th term?

Answer 1

Solution:-
Given : a₁₂ = 47 or a + 11d = 47
a₁₆ = a + 15d and a₈ = a +7d
Now, according to the question
2(a + 7d) + 1 = a + 15d
2a + 14d + 1 = a + 15d
2a - a = 15d - 14d - 1
a = d -1 .................(1)
Substituting the value of 'a' in a + 11d = 47, we get
d - 1 + 11d = 47
12d = 47 + 1
12d = 48
d = 4
Substituting the value of 'd' in a + 11d = 47, we get
a + 11*4 = 47
a = 47 - 44
a = 3
Now
nth term = a + (n - 1)d
= 3 + (n - 1)4
= 3 + 4n - 4
nth term = 4n - 1
Answer.