Question

if SN of AP is (4n-n square) , find AP​

Answer 1

Step-by-step explanation:

$\huge\blue{\underline{\underline{\bf Question:-}}}$

$sn \: of \: AP \: is \: \implies \\ \\ (4n - {n}^{2} ) \\ \\ find \: \: the \: \: AP$

$\huge\blue{\underline{\underline{\bf Answer:-}}}$

$(4n - {n}^{2} ) \\ \\ first \: \: term = a = t1 = (4(1) - 1) = 3 \\ \\ sum \: of \: second \: \: term = (8 - 4) = 4 \\ \\ t2 = Sum \: \: of \: \: second \: \: term - first \: \: term \\ = 4 - 3 = 1 \\ \\ third \: \: term = (4n - {n}^{2}) = (12 - 9) = 3 \\ \\ t3 = 4-3 = -1 \\ t4 = (4n -{n}^{2}) = 16 - 16 = 0$

$A.P\: \: will \: \: be \implies \\ \\ 3,4,3,0....$

Answer 2

Given ,

The sum of n terms of AP is 4n - n²

$\star \: \: \sf S_{1} \: \: or \: \: First \: term = 4(1) - {(1)}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4 - 1\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3 \\ \\ \star \: \: \sf S_{2} = 4(2) - {(2)}^{2} \\ \: \: \: \: \: \: \: \: \: \: = 8 - 4\\ \: \: \: \: \: \: \: \: \: \: = 4$

We know that ,

$\large { \red{ \sf \fbox{ \fbox{ \pink{Second \: term = \sf S_{2} - \sf S_{1}}}}}}$

Substitute the values , we obtain

$\sf \hookrightarrow Second \: term = 4 - 3 \\ \\ \sf \hookrightarrow Second \: term =1$

So , the common difference is (1 - 3) i.e - 2

Therefore , The required AP is 3 , 1 , - 1 , - 3 , ......