The fifth term of an A.P is $20$ and the sum of its seventh and eleventh terms is $64$ . Find the Common Difference.

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Solution

Let the first term of AP be $a$ and common difference be $d$ ,

According to question,

$5 t h$ term is $20$ => $a + 4 d = 20$ .......(1)

And, $a + 6 d + a + 10 d = 64$

=> $2 a + 16 d = 64$

=> $a + 8 d = 32$ .........(2)

From (1) & (2),

$d = 3$ , & $a = 8$

Hence common Difference= $3$

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