Question

Fifth term of an ap is 75 and 8th term is 525 find the sixth term

Answer 1

Given,
$a_{5} = 75 \\ \bf \: i.e. \: a + 4d = 75 \: \: \: \: \: \: \: \: \: \: ...(i) \\ \\ a_{8} = 525 \\ \bf \: i.e. \: a + 7d = 525 \: \: \: \: \: \: \: \: \: ...(ii) \\ \\ a_{6} = (to \: be \: calculated)$




Subtracting both the equations we get,

$\bf \: (a + 4d) - (a + 7d) = 75 - 525 \\ \\ a + 4d - a - 7d = - 450 \\ \\ - 3d = - 450 \\ \\ d = \frac{ - 450}{ - 3} \\ \\ d = 15$

Putting the value of d in equation (i) we get,

a + 4d = 75

a + 4(15) = 75

a + 60 = 75

a = 75 - 60

a = 15

So,

$a_{6} = a + 5d \\ \\ a_{6} = 15 + 5(15) \\ \\ a_{6} = 15 + 75 \\ \\ a_{6} = 90$

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