SOLUTION: the fifteenth term in an arithmetic sequence is 43 and the sum of the first 15 terms of the series is 120. determine the first three terms of the sequence.

Question 881058: the fifteenth term in an arithmetic sequence is 43 and the sum of the first 15 terms of the series is 120. determine the first three terms of the sequence.
Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
the fifteenth term in an arithmetic sequence is 43 and the sum of the first 15 terms of the series is 120. determine the first three terms of the sequence.
T15= a+14d=43 (1)
S15= 15(2a+14d)/2 =120 (2)
15(a+a+14d)/2 =120 by substituting a+14d=43 in (2)
15(a+43)/2=120
a+43=120x2/15
a+43=16
a=16-43 =-27
a+14d=43
-27 +14d = 43
14d=43+27
14d = 70
d=70/14 =5
Answer first terms= -27
Second term = -27+5 =-22
third term = -27+2x5 =-27 +10= -17

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