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Answers
Answer:
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Step-by-step explanation:
Sn = 4n-n²
if we consider n as 1 then
Sn= 4*1-1*1
=4-1
=3
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