Question

find the missing terms, if following are in A. P. 2,_,26,_.

Answer 1

a=2
T3=26
a+(3-1)d=26
2+2d=26
2d=24
d=12
Missing Terms
T2=2+12=14
T4=2+36=38

Answer 2

Let the missing terms be a and b,
We know that If 3 terms for example x,y,z are in A.P, Then, y = (x+z)/2,
And We also knew that,
A.P follows a Common Difference i.e,

Difference between 1st and 2nd term equals to Difference between 3rd and 4th term,
=> 2nd Term - 1st Term = 4th Term - 3rd Term,

Now, let a be between 2 and 26, and b be after 26,
=> Sequence will be 2,a,26,b,

Now, by the first statement,
a = (26+2)/2 = 28/2 = 14,

Now, By 2nd Statement,
14 - 2 = b - 26,
=> 12 = b - 26,
=>b = 38,

Proof :
If this is correct then (a+b)/2 must be 26, Due to the 1st statement,
=> Checking by substituting the values,
=> (14+38)/2
=> (52)/2,
=> 26 = 26,

Therefore the missing terms are 14 and 38 respectively, and the sequence is 2,14,26,38,..... Common difference = 12,

Hope you understand, Have a Great Day !
Thanking you, Bunti 360 !