唔識搵 general terms, 救命, maths

3, 2, 1, 0, -1 ...... is an arithmetic sequence.
The first term, a = 3
The common difference, d = -1

The general term T(n)
= a + (n - 1)d
= 3 + (n - 1)(-1)
= 3 - n + 1
= 4 - n

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14, 10, 6, 2, -2 ..... is also an arithmetic sequence.
The first term, a = 14
The common difference, d = -4

The general term T(n)
= a + (n - 1)d
= 14 + (n - 1)(-4)
= 14 - 4n + 4
= 18 - 4n

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1, 3, 6, 10, 15 ...... is NOT an arithmetic sequence.
The general term a + (n - 1)d

T(1) = 1
T(2) = 3 = 1 + 2
T(3) = 6 = 1 + 2 + 3
T(4) = 10 = 1 + 2 + 3 + 4
T(5) = 15 = 1 + 2 + 3 + 4 + 5

Hence, The general term T(n)
= 1 + 2 + 3 + 4 + ...... + n
= n(n + 1)/2
=