Question

WHICH TERM IS -7ROOT3 OF A.P.5ROOT3,3ROOT3,ROOT3

Answer 1

Given,
$a_{n} = - 7 \sqrt{3} \\ \\ a = 5 \sqrt{3} \\ \\ d = a_{2} - a_{1} \\ d = 3 \sqrt{3} - 5 \sqrt{3} \\ d = - 2 \sqrt{3} \\ \\ n = (to \: be \: calculated)$

Now,

$\bf \: we \: know \: that \\ \bf \: a_{n} = a + (n - 1)d \\ \\ - 7 \sqrt{3} = 5 \sqrt{3} + (n - 1) \times - 2 \sqrt{3} \\ \\ - 7 \sqrt{3} = 5 \sqrt{3} - 2 \sqrt{3} n + 2 \sqrt{3} \\ \\ - 7 \sqrt{3} = 7 \sqrt{3} - 2 \sqrt{3} n \\ \\ - 2 \sqrt{3} n = - 7 \sqrt{3} - 7 \sqrt{3} \\ \\ - 2 \sqrt{3} n = - 14 \sqrt{3} \\ \\ n = \frac{ - 14 \sqrt{3} }{ - 2 \sqrt{3} } \\ \\ \bf \: n = 7$

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