SOLUTION: the first term of an AP is 11 and the sums of the first five and first ten terms respectively are equal in magnitude but opposite in sign. find the second term of the progression.

Algebra ->  Sequences-and-series -> SOLUTION: the first term of an AP is 11 and the sums of the first five and first ten terms respectively are equal in magnitude but opposite in sign. find the second term of the progression.       Log On


   

Question 982131: the first term of an AP is 11 and the sums of the first five and first ten terms respectively are equal in magnitude but opposite in sign. find the second term of the progression.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
the first term of an AP is 11 and the sums of the first five and first ten terms respectively are equal in magnitude but opposite in sign. find the second term of the progression.
Hera a =11
Sn = (n/2)(2a+(n-1)d)
S5 = 5/2(2*11+(5-1)*d)
=5/2(22+4d))

S10 = 10/2(2*11+9*d)
=5(22+9d)
S5= -S10
5/2(22+4d) = -5(22+10d)
22+4d=-2(22+10d)
22+4d=-44-20d
24d= -66
d= -66/24
d=-11/4
T2 = 11+d
T2 = 11-11/4
T2=33/4
11, 33/4,22/4.11/4,0,-11/4, -22/4,-33/4,-44/4,-55/4,