Question

can someone help me?

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given

$S_{n}$ = 7n - 2n² , then

$S_{1}$ = 7(1) - 2(1)² = 7 - 2 = 5

Hence a₁ = 5

Also

$S_{2}$ = 7(2) = 2(2)² = 14 - 8 = 6

$S_{3}$ = 7(3) - 2(3)² = 21 - 18 = 3

$S_{4}$ = 7(4) - 2(4)² = 28 - 32 = - 4

Thus

a₂ = S₂ - S₁ = 6 - 5 = 1

a₃ = S₃ - S₂ = 3 - 6 = - 3

a₄ = S₄ - S₃ = - 4 - 3 = - 7

The first 4 terms of the sequence are

5, 1, - 3, - 7

There is a common difference d between consecutive terms, that is

d = 1 - 5 = - 3 - 1 = - 7 - (- 3) = - 4

The n th term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

Here a₁ = 5 and d = - 4 , thus

$a_{n}$ = 5 - 4(n - 1) = 5 - 4n + 4 = 9 - 4n

In conclusion

a₁ = 5

d = - 4

$t_{n}$ = 9 - 4n