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BaLLatris [955]
3 years ago
10

Guys please help me out ASAP, Due today. I

Mathematics
1 answer:
Mice21 [21]3 years ago
5 0

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

CalculateS_{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

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