Question

find the common difference of the Ap 1/a,1_a/a, 1_2a/a?
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Answer 1

$\cal{AP : } \: \: \tt \frac{1}{a} , \: \frac{1 -a }{a} , \: \frac{1 - 2a}{a}$

$\text{Common Difference =} \: \tt a_2 - a_1 = a_3 – a_2$

So,

$\text{Common Difference of this AP} \\ \\ \to \tt \frac{1 - a}{a} - \frac{1}{a} \\ \\\to \tt \frac{1 - a - 1}{a} = \frac{ \cancel1 - a - \cancel1}{a} \\ \\ \to \tt \frac{ - a}{a} \: \: = \green{- 1} \\ \\\underbrace{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \overbrace{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \to \rm\frac{1 - 2a}{a} - \frac{1 - a}{a} \\ \\ \to \rm \frac{1 - 2a - 1 + a}{a} \\ \\ \to \rm \frac{ -a }{a} \: \: \: = \green{- 1}$

Hence,

• It is concluded that the Common Difference of AP is – 1

Answer 2

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