Question

Very Short Answer Type Questions
1) If 4/5,x, 2 are three consecutive terms of an A.P. then find the value of x.
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Answer 1

$\maltese$Given :-

• 4/5 , x, 2 are the consecutive three terms in A. P  

$\maltese$To find :-

• Value of x

$\maltese$Solution :-

If a, b, c are in A.P since their common difference must be same i.e

c -b = b- a So,

4/5 , x , 2 are in A. P since ,

• a = 4/5
• b = x
• c = 2

Substituting the values ,

c - b = b- a

$2-x =x-\dfrac{4}{5}$

$2+\dfrac{4}{5} =x+x$

$2+ \dfrac{4}{5} = 2x$

$\dfrac{5\times 2+4}{5}= 2x$

$\dfrac{10+4}{5} = 2x$

$\dfrac{14}{5} = 2x$

$\dfrac{7}{5} =x$

So, the value of x is 7/5

$\maltese$V E R F I C A T I O N :-

Since the three terms in A. P are 4/5, 7/5 , 2 So, their common difference must be same

$2-\dfrac{7}{5} =\dfrac{7}{5} -\dfrac{4}{5}$

$\dfrac{5\times 2 -7}{5}=\dfrac{7-4}{5}$

$\dfrac{10-7}{5} =\dfrac{3}{5}$

$\dfrac{3}{5} =\dfrac{3}{5}$

L.H.S = R.H.S

Hence verified!