Question

Find the missing terms of the A.P. : 5, _____ , _____ , 19/2

A) 13/2 , 8
B) 7, 8
C) 15/2 , 7
D) None of these

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Answer 1

Answer:D

A. P. - 5, __ ,__, 19/2.

We just need to find d ( common. Difference).

a = 5

an =19/2

n = 4

an = a + ( n- 1) d

19/2 = 5 +(4-1)d

19/2-5 = 3d

9/2 =3d

d= 3/2

2nd term = a +d =5+ 3/2 =13/2.

3rd term = a +2d = 5 + 2(3/2) =8.

The right option is (A).

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Answer 2

Let the missing terms of AP be "a" and "b".

Thus, AP => 5, a, b, 19/2.

And we know that an algebraic property of AP states that, "The difference between the two consecutive terms of an AP is maintained."

Thus,

a - 5 = b - a

=> 2a - b = 5 ..........(i)

and,

b - a = 19/2 - b

=> 2b - a = 19/2 ..........(*multiply equation by 2*)

=> 4b - 2a = 19 .............(ii)

.

Add (i) and (ii),

3b = 24

=> b = 8. ...........(put in (i))

.

2a - b = 5

=> 2a - 8 = 5

=> 2a = 13

=> a = 13/2.

Thus the missing terms of AP are: 8 and 13/2.

Hence, the correct option is: (A) 13/2, 8.