Question

a,b,c,d and e are 5 integers such that a+b=b+c=c+d=d+e=20/2 and a+b+c+d+e=5024. then d-a is

​

Answer 1

a + b = b + c = c + d = d + e = $\frac{20}{2}$ = 10 ... (A)

a + b = b + c => a = c ... (i)

b + c = c + d => b = d ... (ii)

c + d = d + e => c = e ... (iii)

from (i) and (iii)

a = c = e ... (iv)

a + b + c + d + e = 5024

a + b + a + b + a = 5024 ... (from iv)

a + 2a + 2b = 5024

a + 2(a + b) = 5024

a + 2(10) = 5024 ... (from A)

a + 20 = 5024

a = 5004 ... (v)

substituting in a + b = 10

5004 + b = 10

b = -4994

d = -4994 ... (vi) ... (from ii)

now,

d - a

= -4994 - 5004 ... (from v and vi)

= -9998

Hence, d - a = -9998