Jadhav Theorem
Jadhav Theorem, or Jadhav Arithmetic Theorem, is a theorem derived by Jyotiraditya Jadhav which is applicable for any three consecutive terms of an arithmetic sequence.
Statement
Let 
, 
and 
be three consecutive terms in an arithmetic sequence with common difference 
. Then 
Proof
From difference of squares, the equation 
holds. We can rewrite 
and 
as and , respectively. Now our equation is 
, and rearranging gives us , as desired.
Uses
- This can be used to find the square of any number without a calculator.
- For example, let's find square of
. This number is part of the arithmetic series 
with common difference 
. We can derive 
from Jadhav Theorem. The square of common difference is 4 and the product of 
and 
is 10400 and later adding square of common difference (4) into it will make it 
, so 
- Let's find the square of 406. It is a term of arithmetic progression
with common difference 6. 
can be easily found as 
, and adding square of common difference (36) to this makes it 164836 which is square of 406.
- For example, let's find square of
- This pattern can be used to make equations for unknown quantities of the arithmetic series, as this is in a form of 4 variables then it can be used to make a equation of 4 unknown quantities with other three equations (quadratic equation).
. This number is part of the arithmetic series 
with common difference 
. We can derive 
from Jadhav Theorem. The square of common difference is 4 and the product of 
and 
is 10400 and later adding square of common difference (4) into it will make it 
, so 
with common difference 6. 
can be easily found as 
, and adding square of common difference (36) to this makes it 164836 which is square of 406.This article is a stub. Help us out by expanding it.
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