Question

If in an ap sum of n terms is -3n^2 find its common difference

Answer 1

Answer:

$\red {common \: difference (d)} \green {= -6}$

Step-by-step explanation:

$Given \: in \: an \: A.P \: Sum \: of \: n \: terms \\is \: -3n^{2}$

$S_{n} = -3n^{2}$

$\boxed {\pink {n^{th} \: term = a_{n} = S_{n} - S_{(n-1)}}}$

$a_{n} = -3n^{2} - [- 3(n-1)^{2}]$

$= -3n^{2} + 3(n-1)^{2}$

$= -3n^{2} + 3( n^{2} - 2n + 1 )$

$= -3n^{2} + 3n^{2} - 6n + 3$

$\blue { a_{n} = -6n + 3 }$

$\orange {a_{1}} = -6\times 1 + 3 = \orange {-3}$

$\orange {a_{2}}= -6\times 2 + 3 = -12+3 = \orange {-9 }$

$\green { Common\: difference (d)} = a_{2} - a_{1}\\= -9 - (-3) \\= -9 + 3 = \green {-6}$

Therefore.,

$\red {common \: difference (d)} \green {= -6}$

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Answer 2

Answer:

Step-by-step explanation: