SOLUTION: The 16th term of an A.P. is 40 and the sum of the first 5 terms is 5. Find the sum of the first 50 terms.

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Question 1054074: The 16th term of an A.P. is 40 and the sum of the first 5 terms is 5. Find the sum of the first 50 terms.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B16%5D=a%5B1%5D%2B%2816-1%29%2Ad=40
1.a%5B1%5D%2B15d=40
.
.
S%5B5%5D=%285%2F2%29%28a%5B1%5D%2Ba%5B5%5D%29=5
a%5B1%5D%2Ba%5B5%5D=2
a%5B1%5D%2Ba%5B1%5D%2B%285-1%29%2Ad=2
2a%5B1%5D%2B4d=2
2.a%5B1%5D%2B2d=1
Subtract eq. 1 from eq. 2,
a%5B1%5D%2B2d-a%5B1%5D-15d=1-40
-13d=-39
d=3
So then,
a%5B1%5D%2B2%283%29=1
a%5B1%5D=1-6
a%5B1%5D=-5
So then the sum is,