Question

Guys please help me out ASAP, Due today. I

In an arithmetic sequence Sn = n² - 2n.
Use your formula in 2c to determine the value of
(a) T7 =
(b) Tn=

The formula in 2c : Sn - Sn-1 =Tn

Answer 1

`T_7 = 11`

`T_n = 2n- 3`

Explanation:

Given

`S_n = n^2 -2n`

`T_n = S_n - S_(n-1)`

Solving (a): T7

Substitute 7 for n in
`T_n = S_n - S_(n-1)`

`T_7 = S_7 - S_(7-1)`

`T_7 = S_7 - S_6`

Calculate S7 and S6

`S_n = n^2 -2n`

`S_7 = 7^2 - 2 * 7 = 35`

`S_6 = 6^2 - 2 * 6 = 24`

So:

`T_7 = 35 -24`

`T_7 = 11`

Solving (b): Tn

`T_n = S_n - S_(n-1)`

Where
`S_n = n^2 -2n`

Calculate
`S_(n-1)`

We have:

`S_(n-1) =(n-1)^2 - 2(n-1)`

Open brackets

`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`

So:

`T_n = S_n - S_(n-1)`

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

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

Collect Like Terms

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

`T_n = 2n- 3`