SOLUTION: The sum of 6 consecutive odd numbers is 84. What is the third number in this sequence?

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Question 935511: The sum of 6 consecutive odd numbers is 84.
What is the third number in this sequence?
Found 3 solutions by Alan3354, Fombitz, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of 6 consecutive odd numbers is 84.
What is the third number in this sequence?
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84/6 = 14, the center of the set.
There are 3 integers below 14 and 3 above.
--> 9,11,13,15,17,19

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28N-6%29%2B%28N-4%29%2B%28N-2%29%2B%28N%29%2B%28N%2B2%29%2B%28N%2B4%29=84
6N-6=84
6N=90
N=15
The third number is N-2
N-2=13

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of 6 consecutive odd numbers is 84.
What is the third number in this sequence?
STEP 1:

Use the formula for the sum of an AP (arithmetic sequence) to determine the 1st term

STEP 2:

Use the formula for determining the term value in an AP to find the 3rd term

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