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General Form of an AP

The fourth te...

Question

The fourth term of an A.P. is $11$ . The sum of the fifth and seven terms of the A.P. is $34$ . find its common difference.

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Solution

$T_{4} = 11$
$T_{5} + T_{7} = 34$
$a + 3 d = 11$ ,
$a + 4 d + a + 6 d = 34$
$2 a + 10 d = 34$
$a + 5 d = 17$
$\Rightarrow (a + 5 d) - (a + 3 d) = 17 - 11$
$\Rightarrow 2 d = 6$
$\Rightarrow d = 3$ .

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