The sum of the first twenty terms of an arithmetic progression is 50, and the sum of the next twenty is -50. find the sum of the first hundred terms of the progression.

Question

hartnn · Answer

sum of the next twenty is -50 ---> sum of 1st 40 terms=0(-50+50)
now use the formula for sum of numbers in AP:n/2*(2a+(n-1)*d)
so 10(2a+19d)=50----->'X'
     20(2a+39d)=0------>'Y'
can u solve these two simultaneously to get a and d??
then for sum of 1st 100 terms,just use the same formula and calculate:
50(2a+99d)

anonymous · Answer

@hartnn the answer of my teacher is not matching with both of us..... I also tried in the same way but didn't mathced. Ans. is around -750......

hartnn · Answer

what u got as a and d using my method?

anonymous · Answer

a = - (39/8)

d = - (1/4)

hartnn · Answer

2a=-39d
-39d+19d=5
d=-0.25
a=4.875
50(2*4.875-99*0.25)=-750

hartnn · Answer

a will come positive check

hartnn · Answer

did u find your error? @curiousshubham

anonymous · Answer

yeah i found it........
there was equation: a= (-39d)/2 but while multiplying d with -39 i didn't remove the minus(-) sign... thanks!!!!!!