<PRE><B>Question 903123</B>
3      3       1       0       0
6      4       1       0       0
10     5       1       0
15     6       1
21     7
28     8
36     9
45    10
55    11
66    12
78    13
91    14
105   15
120   16
136   17
153   18
171   19
190   20
210   21
231   22 
253

These are columns differences.
The second column shows that the first column difference increase by one and starts with three.

an = a + (n - 1)1
a6 = 3 + 5*1
A6=3+5=8
here a1=3
lets try a few
S = ½(2a + (n-1)d)n
S = ½(2a + (n-1)d)n
#4(+1)
S4 = ½(6 + (3))4
S4 = 2(9)=18 +3=21
#5(+1)
S5 = ½(6 + (4))5
S5 = ½(10)5=25+3=28
Now for your 20th
#19+1
S = ½(2a + (n-1)d)n
S = ½(6 + (18))19
S = ½(24))19
s20=12*19+3=228+3=231





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