The average of 6 consecutive even numbers is 25. If the next even numb...
Let the first integer be 2x.
Average of 6 consecutive integers: (2x + (2x + 2) + ... + (2x + 10))/6= 12x + 2(1 + 2 + ... + 5) = 12x + 30 = 25 × 6 = 150
⇒ x = 10.
Average of new numbers: (2x + (2x + 2) + ... + (2x + 12) )/ 7 = (14x + 42)/7 = 2x + 6 = 20 + 6 = 26.
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The average of 6 consecutive even numbers is 25. If the next even numb...
Calculation of the New Average
To find the new average after considering the next even number, we first need to determine the 6 consecutive even numbers.
Step 1: Finding the 6 Consecutive Even Numbers
Let's assume the first even number is x. The next 5 even numbers will be x+2, x+4, x+6, x+8, and x+10.
Since the average of these 6 numbers is 25, we can set up an equation:
(x + x+2 + x+4 + x+6 + x+8 + x+10) / 6 = 25
Simplifying the equation:
(6x + 30) / 6 = 25
6x + 30 = 150
6x = 120
x = 20
So, the consecutive even numbers are 20, 22, 24, 26, 28, and 30.
Step 2: Calculating the New Average
Now, we need to include the next even number after 30, which is 32, to find the new average.
Adding 32 to the previous sum of 150:
150 + 32 = 182
Since we now have 7 numbers, we divide the sum by 7 to get the new average:
182 / 7 = 26
Therefore, the new average after considering the next even number is 26. Hence, the correct answer is option 'c) 26'.