Consecutive numbers are numbers each with a difference of 1 from the next.
For example: 0,1,2,3 or 999,1001,1002,1003 or -3,-2,-1,0
When there are 4 consecutive numbers:
a = a b = a+1 c = a+2 d = a+3
a + a+1 + a+2 + a+3 + a+4 = 4a+6
1a) 4a+6 = 130
4a = 124
a = 31
a = 31 b = 32 c = 33 d = 34
1b) 4a+6 = -38
4a = -44
a = -11
a = -11 b = -12 c = -13 d = -14
2) a + b + c = d + 10
a + a+1 + a+2 = a+3 + 10
3a + 3 = a + 13
2a = 10
a = 5
a = 5 b = 6 c = 7 d = 8
3) The answer is 0 as if we use algebra (a = a b = a+1 c = a+2 d = a+3) then we could form the equation of (a + a+3) – (a+ 1 + a+2) and is we were to substitute this, we would find an equation of 2a + 3 – 2a + 3 which equals 0.
4) a + a+1 + a+2 – a+3
= 3a + 3 – a+3
= 2a (double the first consecutive number)