When we have a sequence of consecutive odd numbers, each number is formed by adding a fixed difference to the previous number. In this case, since we are dealing with odd numbers, the fixed difference between consecutive terms is 2.
For example, if we start with the first term, which is 11, we can find the second term by adding 2: 11 + 2 = 13. Similarly, we can find the third term by adding 2 to the second term: 13 + 2 = 15. We can continue this process to find the remaining terms.
In the given problem, we are told that the sum of these five consecutive odd numbers is 85. We can use this information to find the middle term.
The sum of an arithmetic series can be calculated using the formula: sum = (n/2) * (first term + last term), where n is the number of terms.
Substituting the given values, we have:
85 = (5/2) * (11 + last term).
Simplifying further, we get:
85 = (5/2) * (11 + last term)
85 = (5/2) * (11 + last term)
170 = 5 * (11 + last term)
34 = 11 + last term
last term = 34 - 11
last term = 23.
Therefore, the last term of the sequence is 23.
To find the middle term, we can use the formula: middle term = (first term + last term) / 2.
Plugging in the values, we have:
middle term = (11 + 23) / 2
middle term = 34 / 2
middle term = 17.
Hence, the value of the middle term among the five consecutive odd numbers is 17.
Let's denote the first odd number in the series as "x." Since these are consecutive odd numbers, the next four odd numbers will be x + 2, x + 4, x + 6, and x + 8, respectively.
According to the problem, the sum of these five consecutive odd numbers is 85. So, we can set up the equation:
x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 85
Now, let's simplify and solve for x:
5x + 20 = 85
Subtract 20 from both sides:
5x = 85 - 20
5x = 65
Now, divide both sides by 5 to solve for x:
x = 65 / 5
x = 13
So, the first odd number is 13. Now, we can find the other four consecutive odd numbers:
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[tex]\huge \color{red} \boxed{ \colorbox{white}{Ans♡˖꒰ᵕ༚ᵕ⑅꒱}}[/tex]
The sum of five consecutive odd numbers is 85.
When we have a sequence of consecutive odd numbers, each number is formed by adding a fixed difference to the previous number. In this case, since we are dealing with odd numbers, the fixed difference between consecutive terms is 2.
For example, if we start with the first term, which is 11, we can find the second term by adding 2: 11 + 2 = 13. Similarly, we can find the third term by adding 2 to the second term: 13 + 2 = 15. We can continue this process to find the remaining terms.
In the given problem, we are told that the sum of these five consecutive odd numbers is 85. We can use this information to find the middle term.
The sum of an arithmetic series can be calculated using the formula: sum = (n/2) * (first term + last term), where n is the number of terms.
Substituting the given values, we have:
85 = (5/2) * (11 + last term).
Simplifying further, we get:
85 = (5/2) * (11 + last term)
85 = (5/2) * (11 + last term)
170 = 5 * (11 + last term)
34 = 11 + last term
last term = 34 - 11
last term = 23.
Therefore, the last term of the sequence is 23.
To find the middle term, we can use the formula: middle term = (first term + last term) / 2.
Plugging in the values, we have:
middle term = (11 + 23) / 2
middle term = 34 / 2
middle term = 17.
Hence, the value of the middle term among the five consecutive odd numbers is 17.
So, It is 11 + 16 + 18 + 23 + 17 = 85
-Aaxansha ✨
Verified answer
Answer:
Let's denote the first odd number in the series as "x." Since these are consecutive odd numbers, the next four odd numbers will be x + 2, x + 4, x + 6, and x + 8, respectively.
According to the problem, the sum of these five consecutive odd numbers is 85. So, we can set up the equation:
x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 85
Now, let's simplify and solve for x:
5x + 20 = 85
Subtract 20 from both sides:
5x = 85 - 20
5x = 65
Now, divide both sides by 5 to solve for x:
x = 65 / 5
x = 13
So, the first odd number is 13. Now, we can find the other four consecutive odd numbers:
13, 15, 17, 19 and 21