Ch 5 , Arithmetic progression , Q If 8n =4n - n2, find an

1.	Ch 5 , Arithmetic progression , Q If 8n =4n - n2, find an
Answer» Sum of the first n term = 4n - n^2 Sn = 4n-n^2 then n=1 ,4×1-1^2 =3 the sum of first term is 3 then n=2 , 4×2-2^2=4 the sum of 2 term is 4 then second term = sum of 2 term - sum of 1 term = 4 -3 = 1 then a = 3 , a+d=1 then d =-2 then n term is a+ (n-1)×d = 3+(n-1)×-2 = 5 -2n We have given thatSum of the first n terms = 4n – n2⇒ Sn\xa0= 4n – n2Sn –1\xa0= 4(n – 1) – (n – 1)2= (4n – 4) – (n2\xa0+ 1 – 2n)= 4n – 4 – n2\xa0– 1 + 2n= 6n – n2\xa0– 5∴ nth term = Sn\xa0– Sn – 1= (4n – n2) – (6n – n2\xa0– 5)= 4n – n2\xa0– 6n + n2\xa0+ 5= 5 –2n.

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