SOLUTION: The first term of an arithmetical progression is 11 and the sums of the first five and the first ten terms respectively are equal in magnitude but different in sign.Find the second

Question 909311: The first term of an arithmetical progression is 11 and the sums of the first five and the first ten terms respectively are equal in magnitude but different in sign.Find the second term of the progression.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
The first term of an arithmetical progression is 11 and the sums of the first five and the first ten terms respectively are equal in magnitude but different in sign.Find the second term of the progression.
a=11
S5 =-S10
sum of n terms

Sn = n/2(2a+(n-1)d)
S5 =5/2(2*11+(5-1)d)
=5/2(22+4d)
=5(11+2d)

S10= 10/2(22+(9*d))
=5(22+9d)
5(11+2d)=-5(22+9d)
55+10d=-110-45d
-55d=165
d=-3
S2= 2/2(2*11-3)
=19

S2=19
RELATED QUESTIONS
the first term of an AP is 11 and the sums of the first five and first ten terms... (answered by mananth)

the first term of an AP is 11 and the sums of the first five and first ten terms... (answered by MathTherapy)

The sum of the 4th and 6th term of an arithmetical progression is 42.the sum of the 3rd... (answered by mananth)

Given that the first term of an Arithmetical Progression is 7 and its 10th term is twice... (answered by mananth)

The nth term of an arithmetical progression is n and the nth term is m. Find the first... (answered by josgarithmetic)

The nth term of an arithmetical progression is n and the nth term is m. Find the first... (answered by KMST)

Find the difference between the sums of the first ten terms of the Geometrical and... (answered by MathLover1,MathTherapy)

The first term of an arithmetic progression is 12 and the sum of the first 16 terms is... (answered by greenestamps)

In an arithmetic progression, the sum of the first ten terms is 50 and the 5th term is... (answered by MathTherapy)