what is sum of 7 consecutive odd integers?
Which integers?
If x = smallest integer,
x + (x+2) + (x+4)… + (x+12) = ?
sum of 1st 7 odds is 7^2 = 49
so, if you start with 2k+1 instead of 1, then each odd number is increased by 2k, so you wind up with 7*2k + 49
check: let k=5 and you have
11+13+15+17+19+21+23 = 119 = 7*10+49
To find the sum of any consecutive sequence, it is important to first identify the pattern and then use the appropriate mathematical formula. In this case, we are looking for the sum of 7 consecutive odd integers.
Consecutive odd integers follow a pattern where each number is obtained by adding 2 to the previous number. So, the sequence would be something like this: x, x + 2, x + 4, x + 6, x + 8, x + 10, x + 12.
To find the sum of this sequence, we can use the formula for the sum of an arithmetic series, which is:
Sum = (n / 2)(first term + last term)
Since we want the sum of 7 numbers, n = 7. The first term (x) is the starting integer, and the last term is the 7th number in the sequence (x + 12).
Putting this information into the formula, we get:
Sum = (7 / 2)(x + x + 12)
Simplifying, we have:
Sum = (7 / 2)(2x + 12) = 7x + 42
Therefore, the sum of 7 consecutive odd integers is 7x + 42.
Please note that since you haven't provided a specific starting number (x), I have represented it as x in the equation. Once you have a value for x, you can substitute it into the equation to find the sum.