Question

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

Answer 1

`T_n = 2n -3`

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`