Question

The sum, S, of 4 consecutive odd integers can be represented by the equation: a) S = 4n - 12 b) S = 4n + 12 c) S = 4n - 4 d) S = 4n + 4

Answer 1

Answer B

Explanation:

• Let's start by defining the first odd integer as "n."

• The next three consecutive odd integers can be represented as

n + 2, n + 4, and n + 6 because consecutive odd integers are 2 units apart from each other.

• Now, let's find their sum S:

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

Combine like terms by adding the numbers.

S = n + n + 2 + n + 4 + n + 6

Combine the "n" terms.

S = 4n + 2 + 4 + 6

Add the constants.

S = 4n + 12

So, using this method, we also arrive at the equation:

S = 4n + 12

Answer 2

b) S = 4n + 12

Explanation:

The sum of 4 consecutive odd integers is found by:

n = 1st odd integer

n+2 = 2nd odd integer

n+4 = 3rd odd integer

n+6 = 4th odd integer

Sum = n + n+2 + n+4 + n+ 6

Combine like terms.

= 4n + 12