Home > Algebra > Problem-Solving Models

The sum of 6 consecutive integers is 393. What is the third number In this sequence?

Answer 1

Isaiah Anthony

Let's define the first integer as #x#. Then the next five consecutive integers would be:

#x + 1#, #x + 2#, #x + 3#, #x + 4# and #x + 5#.

The sum of these six integers is 393 so we can write:

#x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 393#

#6x + 1 + 2 + 3 + 4 + 5 = 393#

#6x + 15 = 393#

#6x + 15 - 15 = 393 - 15#

#6x + 0 = 378#

#(6x)/6 = 378/6#

#x = 63#

Because the first integer is 63 then the third would be #x + 2# or #63 + 2 = 65#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Genesis Allen

Let the third integer in the sequence be ( x ). The sum of the six consecutive integers can be represented as: ( x-2 + x-1 + x + x+1 + x+2 + x+3 = 393 ). Solving this equation yields ( x = 65 ). Therefore, the third number in the sequence is ( 65 ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.