SOLUTION: Find the sum of the first thirty terms of the following arithmetic series: 16+25+34+43...

Question 137342: Find the sum of the first thirty terms of the following arithmetic series:
16+25+34+43...
Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the sum of the first thirty terms of the following arithmetic series:
16+25+34+43...
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Find the 30th term:
a(30) = a(1)+29(9)
a(30) = 16+ 261 = 277
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S(30) = (30/2)(16+277) = 4395
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Cheers,
Stan H.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Your series looks like
1st term : 16=16=16+9(1-1)
2nd term : 25=16+9=16+9(2-1)
3rd term : 34=16+9+9=16+9(3-1)
4th term : 43=16+9+9+9=16+9(4-1)
.
.
.
30th term : 261=16+9(29)=16+9(30-1)
The sum of all those terms would be then the sum of 30*16 since there are 30 sixteens added plus 9 times the sum from 1 to 29.
The sum from 1 to n equals n(n+1)/2.
The sum from 1 to 29 equals 29(30)/2=435.
The total sum is then 30*16 (480) plus 9*435 (3915) and equals 4395.

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