SOLUTION: Find the first term of an A.p if the 5th term is 28 and sum of the first 17th term is Zero

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Question 858285: Find the first term of an A.p if the 5th term is 28 and sum of the first 17th term is Zero
Answer by mananth(16946) About Me  (Show Source):
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Find the first term of an A.p if the 5th term is 28 and sum of the first 17th term is Zero
tn = a+(n-1)d
28 = a+4d
a+4d= 28....................(1)
Sn = n/2( 2a+(n-1)d))
0= (17/2)(2a+16d)
0= 17(2a+16d)
34a+272d=0
/34
a+8d=0.....................(2)
subtract (2) from (1)
we get -4d=28
d= -7
Now a+4d=28
a+4*(-7)=28
a-28=28
a=56