Question

Guys please help me out ASAP

Answer 1

Answer:

$T_7 = 11$

$T_n = 2n- 3$

Step-by-step 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

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

$T_n = 2n- 3$