If 4/5, a, 2 are three consecutive terms of an . . .

Question : If 4/5, a, 2 are three consecutive terms of an A.P., then find the value of a.

Doubt by Lakshay

Solution : 

Method I 

4/5, a, 2 are in AP (Given)

Here 

First Term (A) = 4/5 = 0.8

Third Term (A₃) = 2

We know, 
a_n=a+(n-1)d
A₃=A+(3-1)d
2=0.8+2d
2-0.8=2d
1.2=2d
1.2/2=d
0.6=d

Now 
A₂=A+d
a=0.8+0.6
a=1.4 
OR
a=14/10
a=7/5

Method II

4/5, a, 2 are in AP (Given)
0.8, a, 2 are in AP

A₁=0.8
A₂=a
A₃=2

A₂=(A₁+A₃)/2
a=(0.8+2)/2
a=(2.8)/2
a=1.4
a=14/10
a=7/5