Question

If – 5/7,a,2 are consecutive terms in an Arithmetic progression, then the value of ‘a’ is-

A. 9/7

B. 9/14

C. 19/7

D. 19/14​

Answer 1

The answer is B. 9/14

Step-by-step explanation:

Given terms are consecutive, the difference between the first and the second term and the difference between the third and second term will be the same.

1st term = -5/7

2nd term = a

3rd term = 2

Thus, we can write,

$a-(\frac{-5}{7}) = 2-a$

This is an equation in variable 'a'.

$a+\frac{5}{7} = 2-a$

Taking LCM

$\frac{7a+5}{7} = 2-a$

Cross multiplication would give

$7a+5= 7\times (2-a)$

$7a+5= 14-7a$

$7a+ 7a= 14-5$

$14a= 9$

$a = \frac{9}{14}$

Answer 2

Given:

The three consecutive terms of an A.P are -5/7, a, and 2.

To Find:

The value of a is?

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 a, Common difference 'd' and nth term t n is given by the formula.

=>$T_{n} = a+ (n-1)d$

2. Let T1, T2, T3, T4, .., Tn be n terms of an A.P. According to the properties of Arithmetic Progression,

=> T2 - T1 = T3 - T2 = T4 - T3 = T5 - T4 = .. = Tn - Tn-1.

3. Using the property mentioned above we can obtain a relation between the three consecutive terms.

=> a -(-5/7) = 2 - a, ( Solve for value of a ).

=> a + 5/7 = 2 - a,

=> a + a + 5/7 = 2,

=> 2a = 2 - 5/7,

=> 2a = (14-5)/7,

=> 2a = 9/7,

=> a = 9/(7x2),

=> a = 9/14.

Therefore, the value of a is 9/14. Option B is the correct answer.