SOLUTION: the first and the last terms of an arithmetic series are 25 and 197. find the sum of 10th term of the series

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Question 1086736: the first and the last terms of an arithmetic series are 25 and 197. find the sum of 10th term of the series


Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
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Since the number of therms is not given in the condition, the solution is IMPOSSIBLE.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
the first and the last terms of an arithmetic series are 25 and 197. find the sum of 10th term of the series
S%5Bn%5D+=+%28n%2F2%29%28a%5B1%5D+%2B+a%5Bn%5D%29 ------- Formula for the sum of an AP
S%5B10%5D+=+%2810%2F2%29%2825+%2B+197%29 ----- Substituting 10 for n, 25 for a1, and 197 for an
Sum of the 1st 10 terms, or: 

OR

1st term, or a1 = 25
Last term, or an = 197
an = a1 + (n - 1)d
an = 25 + dn – d
197 = 25 + dn – d ------ Substituting 197 for an
172 = dn – d ------ eq (i)

S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29 ------ Formula for the sum of an AP
S%5B10%5D+=+%2810%2F2%29%282%2825%29+%2B+dn+-+d%29 ----- Substituting 10 for n, and 25 for a1
S%5B10%5D+=+5%2850+%2B+dn+-+d%29
S%5B10%5D+=+5%2850+%2B+172%29 ------ Substituting 172 for dn – 5
Sum of the 1st 10 terms, or: