Consecutive number groups

Determine the group of numbers for which the following relations hold:
a) The sum of the searched three consecutive even numbers equals 978.
b) The sum of the searched four consecutive odd numbers equals 312.

Final Answer:

a =  324
b =  326
c =  328
x =  75
y =  77
z =  79
w =  81

Step-by-step explanation:

$$\begin{gathered} a+(a+2)+(a+4)=978 \\ 3a=972 \\ a=\frac{972}{3}=324 \\ a=324 \end{gathered}$$

$b=a+2=324+2=326$

$c=b+2=326+2=328$

$$\begin{gathered} x+(x+2)+(x+4)+(x+6)=312 \\ 4x=300 \\ x=\frac{300}{4}=75 \\ x=75 \end{gathered}$$

$y=x+2=75+2=77$

$z=y+2=77+2=79$

$w=z+2=79+2=81$

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