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Instructions
Answer the questions based on the following information. A series $$S_{1}$$ of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series $$S_{2}$$, the nth term is defined as the difference between the (n+1)th term and the nth term of series $$S_{1}$$, $$S_{2}$$ is an arithmetic progression with a common difference of 30.
Solution
Assume the first series as a,b,a/2,c,a+20
and second series as x1,x2,x3,x4
x1=b-a, x2= a/2-b, x3=c-a/2, and x4=a+20-c
x2-x1=30 => 3a-4b=60
and x4-x3=30 => 3a-4c=20
and x4-x2=60 => a-2c+2b=80
Solving we get, a=100, b=60, and c=70
S1= 100,60,50,70,120
S2 = -40, -10, 20, 50
Sum = 20
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