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The sum of the first n terms of a sequence is given by: $S_{n}= n(23 - 3n)$. Calculate the 15th term of the sequence.
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Find the type of a pattern then derive the formula of the nth term

substituting n=1, a= 20

n=2, sum=34

n=3, sum=42

n=4, sum=44,    a=20

a1=34-20=12

a2= 42-34= 8

a3= 44-42= 2

Hence it is an arithmetic pattern, constant difference= d= 6

Tn= a + (n-1)d

T15 = 20 + (15-1)6 = 104
by Diamond (44,170 points)

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