find the ap in which 12th term is 49 and 8 th term is 12 more than 5th t
Answers
Solution:-
Given
=> T₁₂ = 49
=> T₈ = 12 + T₅
Formula
Tₙ = a + ( n - 1 )d
Now Take
=>T₁₂ = 49
=> 49 = a + ( 12 - 1 )d
=> 49 = a + 11d ......( i )
Now Take
=> T₈ = 12 + T₅
=> a + ( 8 - 1 )d = 12 + a + ( 5 - 1 )d
=> a + 7d = 12 + a + 4d
=> a - a - 12 = 4d - 7d
=> 0 - 12 = - 3d
=> 12 = 3d
=> d = 4
Now put the value of d on ( i )st equation
=> a + 11d = 49
=> a + 11 × 4 = 49
=> a + 44 = 49
=> a = 49 - 44
=> a = 5
Ap we get
=> 5 , 9 , 13 , 17 , 21 ,...............
(Question)
➡ Find the A.P. in which 12th term is 49 and 8th term is 12 more that 5th term.
(Answer)
➡ The A.P. is 5, 9, 13, 17, 21......
(Solution)
Let,
First term = a
Common difference = d
Nth term of an A.P.
= a + (n - 1)d
So,
12th term = a + (12 - 1)d
= a + 11d
➡ a + 11d = 49 ..... (i)
8th term = a + (8 - 1)d = a + 7d
5th term = a + (5 - 1)d = a + 4d
Given that, 8th term is 12 more that 5th term.
So,
8th term - 5th term = 12
➡ a + 7d - a - 4d = 12
➡ 3d = 12
Dividing both sides by 3, we get,
➡ d = 4
Putting the value of d in equation (i), we get,
➡ a + 11 × 4 = 49
➡ a + 44 = 49
➡ a = 5
Hence,
a = 5
d = 4
Therefore, the A.P will be,
= a, a + d, a + 2d...
= 5, 9, 13, 17, 21...
(Learn More)
➡ A.P. stands for Arithmetic Progression. It is a sequence in which difference between two consecutive terms in the sequence is same(constant)