Question

find the common difference of AP whose Sn is Sn=n2-n ?​

Answer 1

Answer:-

Sn-1 = a(n-1)^2 + b(n-1)

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1》an^2 + bn - an^2 + 2an - a - bn + b

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1》an^2 + bn - an^2 + 2an - a - bn + b》2an - a + b

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1》an^2 + bn - an^2 + 2an - a - bn + b》2an - a + b__________________________

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1》an^2 + bn - an^2 + 2an - a - bn + b》2an - a + b__________________________If n = 1

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1》an^2 + bn - an^2 + 2an - a - bn + b》2an - a + b__________________________If n = 1a1 》2a - a + b

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1》an^2 + bn - an^2 + 2an - a - bn + b》2an - a + b__________________________If n = 1a1 》2a - a + bIf n = 2

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1》an^2 + bn - an^2 + 2an - a - bn + b》2an - a + b__________________________If n = 1a1 》2a - a + bIf n = 2a2 》 4a - a + b

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1》an^2 + bn - an^2 + 2an - a - bn + b》2an - a + b__________________________If n = 1a1 》2a - a + bIf n = 2a2 》 4a - a + b》d = a2 - a1

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1》an^2 + bn - an^2 + 2an - a - bn + b》2an - a + b__________________________If n = 1a1 》2a - a + bIf n = 2a2 》 4a - a + b》d = a2 - a1= 4a - a + b - 2a + a - b

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1》an^2 + bn - an^2 + 2an - a - bn + b》2an - a + b__________________________If n = 1a1 》2a - a + bIf n = 2a2 》 4a - a + b》d = a2 - a1= 4a - a + b - 2a + a - b= 2a

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1》an^2 + bn - an^2 + 2an - a - bn + b》2an - a + b__________________________If n = 1a1 》2a - a + bIf n = 2a2 》 4a - a + b》d = a2 - a1= 4a - a + b - 2a + a - b= 2a》Hence common difference is 2a

Sn-1 = a(n-1)^2 + b(n-1)= a(n^2-2n+1) + bn -b= an^2 - 2an + a + bn - b___________________________An = Sn - Sn-1》an^2 + bn - an^2 + 2an - a - bn + b》2an - a + b__________________________If n = 1a1 》2a - a + bIf n = 2a2 》 4a - a + b》d = a2 - a1= 4a - a + b - 2a + a - b= 2a》Hence common difference is 2a☺ Hope this Helps ☺

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