Question

If 5 times the 5th term of an



a.P. Is equal to 7 times the 7th term , then the 12th term of the



a.P. Will be?

Answer 1

Answer:

ans-0

Step-by-step explanation:

5(a5)=7(a7)

5{a+(n-1)d}=7{a+(n-1)d}

5{a+(5-1)d}=7{a+(7-1)d}

5(a+4d)=7(a+6d)

5a+20d=7a+42d

5a-7a=42d-20d

-2a=22d

a=22d/-2

a= -11d-------(1)

then,

a12=a+(n-1)d

=a+(12-1)d

=a+11d

= -11d +11d [from eq. 1]

a12=0

Answer 2

Given:

In an Arithmetic progression, the value of the 5 times the 5th term is equal to the value of  7 times the 7th term.

To Find:

The value of the 12th term will be?

Solution:

The given problem can be solved using the concepts of Arithmetic Progression.

1. The nth term of an A.P with the first term as a Common difference as d, and the number of terms n is given by the formula:

=> nth term of an A.P = Tn = a + (n-1)d.

2. The value of the 7th term and the 5th term can be calculated by using the above formula,

=> 5th term = a + 4d,

=> 7th term = a + 6d.

3. 5 times the 5th term is equal to 7 times the 7th term. Hence the equation will be,

=> 5( a + 4d ) = 7 ( a + 6d ),

=> 5a + 20d = 7a + 42d,

=> 7a - 5a + 42d - 20d = 0,

=> 2a + 22d = 0,

=> 2(a + 11d) = 0,

=> a + 11d = 0,

=> a = -11d. ( Asume as equation 1 )

4. The value of the 12th term can be obtained using the above relation.

=> t12 = a + (12-1)d,

=> t12 = a + 11d,

=> t12 = -11d + 11d. ( Since a = -11d ),

=> t12 = 0.

Therefore, the value of the 12th term of the A.P is 0.