Find the greatest possible value for a+b+c+d if b is a positive integer and a, b,c, d satisfy the system of equations a+b=c

b+c=d

c+d=a

Step-by-step explanation:

The given system of equations is now reduced:

1) , , , Given

2) By 1)

3) 2) in 1)

4) By 1)

5) 4) in 3)

6) Algebra

7) Algebra

8) 7) in 4)/Algebra

9) 7) and 8) in 2)/Algebra

10) 9), 1), 7) and 8)/Algebra/Result

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2