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

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 Click here to see ALL problems on Sequences-and-series 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(57219)   (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... ------------- Find the 30th term: a(30) = a(1)+29(9) a(30) = 16+ 261 = 277 ------------------------- S(30) = (30/2)(16+277) = 4395 ================================ Cheers, Stan H. Answer by Fombitz(13828)   (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.