Question

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Answer 1

Step-by-step explanation:

Refer this page for the solution

Answer 2

Answer:

The AP is 3, 1, -1, -3,..........

Step-by-step explanation:

We are given,

Sn = 4n - n²

Thus,

S(1) = a1

when n = 1

S(1) = 4(1) - 1²

S(1) = 4 - 1 = 3

Thus,

a1 = 3 ----- 1

Now,

S(2) = a1 + a2

when n = 2

S(2) = 4(2) - 2²

S(2) = 8 - 4 = 4

a1 + a2 = 4

From eq.1 we get,

3 + a2 = 4

a2 = 4 - 3

a2 = 1 ----- 2

Now,

S(3) = a1 + a2 + a3

when n = 3

S(3) = 4(3) - 3²

S(3) = 12 - 9

S(3) = 3

a1 + a2 + a3 = 3

From eq.1 and eq.2 we get,

3 + 1 + a3 = 3

4 + a3 = 3

a3 = 3 - 4

a3 = -1 ------ 3

S(4) = a1 + a2 + a3 + a4

when n = 4

S(4) = 4(4) - 4²

S(4) = 16 - 16

S(4) = 0

So,

a1 + a2 + a3 + a4 = 0

From eq.1, eq.2 and eq.3 we get,

3 + 1 + (-1) + a4 = 0

3 + a4 = 0

a4 = -3

Thus,

The AP is 3, 1, -1, -3,..........

Hope it helped and believing you understood it........All the best