lebavabi lebavabi
  • 14-03-2021
  • Mathematics
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In an arithmetic sequence Sn=n^2SN=N^2-2N .USE formula (Tn=Sn-Sn-1) to determine the value of Tn​

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MrRoyal
MrRoyal MrRoyal
  • 19-03-2021

Answer:

[tex]T_n = 2n -3[/tex]

Step-by-step explanation:

Given

[tex]S_n = n^2- 2n[/tex]

[tex]T_n = S_n - S_{n-1[/tex]

Required

Find [tex]T_n[/tex]

[tex]S_n = n^2- 2n[/tex]

Calculate [tex]S_{n-1[/tex]

[tex]S_{n-1} = (n-1)^2- 2(n-1)[/tex]

[tex]S_{n-1} = n^2-2n+1- 2n+2[/tex]

[tex]S_{n-1} = n^2-2n- 2n+1+2[/tex]

[tex]S_{n-1} = n^2-4n+3[/tex]

[tex]T_n = S_n - S_{n-1[/tex] becomes

[tex]T_n = n^2 - 2n - (n^2 - 4n +3)[/tex]

[tex]T_n = n^2 - 2n - n^2 + 4n -3[/tex]

[tex]T_n = n^2 - n^2- 2n + 4n -3[/tex]

[tex]T_n = 2n -3[/tex]

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