The sum of 5 consecutive odd numbers is 135

Asked by maham237 @ 09/01/2021 in Mathematics viewed by 344 People

The sum of 5 consecutive odd numbers is 135. What is the second number in this sequence?

Answered by maham237 @ 09/01/2021

When you are confronted by a question like this, you can make a simple equation, combine like terms, isolate the variable, and solve.
"5 consecutive odd numbers" basically means x + (x + 2) + (x + 4) + (x + 6) + (x + 8). Each time you add 2 more to ensure there's no even numbers. Otherwise, it wouldn't be only consecutive odd numbers.
We are told the sum of these numbers is 135. This means x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135.

(x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135
This might seem a bit intimidating, but there's actually only a couple steps.

Step 1: Combine like terms.
In this case, the like terms are the 5 times x appears and the numbers 0, 2, 4, 6, and 8.
x + x + x + x + x = 5 • x, or 5x.
0 + 2 + 4 + 6 + 8 = 20
So by combining like terms, we can simplify (x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135 down to just 5x + 20 = 135.

Step 2: Isolate the variable.
Now we just have to isolate x. The value of x is the lowest term in the sequence.
5x + 20 = 135
To isolate x, first subtract 20 from both sides. Then, divide both sides by 5.
5x + 20 - 20 = 5x
135 - 20 = 115
5x = 115
5x / 5 = x
115 / 5 = 23
x = 23
The lowest term in the sequence is 23.

Step 3 (Last step!): Identify all numbers in the sequence.
Now that we know x, we can find the rest of the numbers in the sequence by plugging the lowest value into the original equation we created.
(x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135
(23 + 0) + (23 + 2) + (23 + 4) + (23 + 6) + (23 + 8) = 135
23 + 0 = 23 This is the first and lowest term in the sequence.
23 + 2 = 25 This is the second term in the sequence.
23 + 4 = 27 This is the third term in the sequence.
23 + 6 = 29 This is the fourth term in the sequence.
23 + 8 = 31 This is the fifth and last term in the sequence.
Now we know the sequence is 23, 25, 27, 29, 31.

Finding the Answer:
To find the answer, locate the second term in this sequence.
23, 25, 27, 29, 31
The second term is 25.
This is the answer.

Answer:
25

Hope this helps!

The sum of 5 consecutive odd numbers is 135

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