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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Mathematics Adela 4 years 2021-08-25T09:28:38+00:00 2021-08-25T09:28:38+00:00 1 Answers 24 views 0

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

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Vodka · Answer 1 · 2021-08-25T09:30:27+00:00

Vodka

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2021-08-25T09:30:27+00:00 August 25, 2021 at 9:30 am

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Answer:

$T_n = 2n -3$

Step-by-step explanation:

Given

$S_n = n^2- 2n$

$T_n = S_n - S_{n-1$

Required

Find $T_n$

$S_n = n^2- 2n$

Calculate $S_{n-1$

$S_{n-1} = (n-1)^2- 2(n-1)$

$S_{n-1} = n^2-2n+1- 2n+2$

$S_{n-1} = n^2-2n- 2n+1+2$

$S_{n-1} = n^2-4n+3$

$T_n = S_n - S_{n-1$ becomes

$T_n = n^2 - 2n - (n^2 - 4n +3)$

$T_n = n^2 - 2n - n^2 + 4n -3$

$T_n = n^2 - n^2- 2n + 4n -3$

$T_n = 2n -3$