Question

If n represents an odd integer,write expressions in terms of n that represents the next three consecutive odd integers.If the four consecutive odd integers have the sum of 56,find the numbers

Answer 1

N
N+2
N+4
N+6

That would be the answer for the first sequence.

Your second question--the integers would be 11,13,15, and 17

Answer 2

Every second integer is odd.  (The ones in between them are even.)

If you promise that 'n' is odd, then the next odd ones
are (n+2), (n+4), and (n+6) .

We need to add them all up:

   n + (n+2) + (n+4) + (n+6)  =  4n + 12

Now you're telling me that the sum is 56.  Knowing that, I can
figure out what 'n' is, and once I know  'n', I can fiugure out all
four of the numbers.

                                           4n + 12 = 56

Subtract  12  from each side:      4n = 44

Divide each side by  4 :                 n = 11

The four consecutive odd integers are:

   n . . . . . 11
   n+2 . . . 13
   n+4 . . . 15
   n+6 . . . 17 .


Check the answer:

Add up  (11 + 13 + 15 + 17)  =   56          yay !