Question

Find the common difference of A.P.4 1/9,4 2/9,4 1/3

Answer 1

AP : 4 $\frac{1}{9}$, 4 $\frac{2}{9}$, 4 $\frac{1}{3}$

_________ [ GIVEN ]

• We have to find the common difference.

___________________________

Now..

$a_{1}$ = 4 $\frac{1}{9}$

=> $\frac{9\:\times\:4\:+\:1}{9}$

=> $\frac{36\:+\:1}{9}$

→ $\frac{37}{9}$

$a_{2}$ = 4 $\frac{2}{9}$

=> $\frac{9\:\times\:4\:+\:2}{9}$

=> $\frac{36\:+\:2}{9}$

→ $\frac{38}{9}$

$a_{3}$ = 4 $\frac{1}{3}$

=> $\frac{3\:\times\:4\:+\:1}{3}$

=> $\frac{12\:+\:1}{3}$

→ $\frac{13}{3}$

____________________________

Common difference = $a_{2}$ - $a_{1}$ = $a_{3}$ - $a_{2}$

Put the values..

→ $\frac{38}{9}$ - $\frac{37}{9}$ = $\frac{13}{3}$ - $\frac{38}{9}$

→ $\frac{38\:-\:37}{9}$ = $\frac{39\:-\:38}{9}$

→ $\frac{1}{9}$ = $\frac{1}{9}$

_____________________________

Common difference = 1/9

_________ [ ANSWER ]

_____________________________

Answer 2

ans

1/9 is common difference