SOLUTION: How do I find the 20th term in the following sequence: 3, 6, 10, 15, 21...

Question 903123: How do I find the 20th term in the following sequence: 3, 6, 10, 15, 21...
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
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 = �(2a + (n-1)d)n
S = �(2a + (n-1)d)n
#4(+1)
S4 = �(6 + (3))4
S4 = 2(9)=18 +3=21
#5(+1)
S5 = �(6 + (4))5
S5 = �(10)5=25+3=28
Now for your 20th
#19+1
S = �(2a + (n-1)d)n
S = �(6 + (18))19
S = �(24))19
s20=12*19+3=228+3=231

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