The sum of 4 consecutive odd numbers is 296. Write an equation and solve it to find the second highest number.
brute force way:
n + n+2 + n+4 + n+6 = 296
using progressions:
4/2 (2n+3*2) = 296
In either case solve for n, and the next number is n+2
Let's call the first odd number x. Since the numbers are consecutive odd numbers, we can express the other three numbers as (x+2), (x+4), and (x+6).
We know that the sum of these four numbers is 296, so we can set up the equation:
x + (x+2) + (x+4) + (x+6) = 296
Simplifying the equation, we can combine like terms:
4x + 12 = 296
Next, let's isolate the variable x:
4x = 296 - 12
4x = 284
Divide both sides of the equation by 4:
x = 284 / 4
x = 71
Therefore, the second highest number is (x+4) = 71 + 4 = 75.
To solve this problem, we first need to represent the consecutive odd numbers mathematically. Let's assume that the first odd number is x.
Since we are dealing with consecutive odd numbers, the second, third, and fourth numbers can be represented as x + 2, x + 4, and x + 6, respectively.
We are given that the sum of these four consecutive odd numbers is 296. So we can write the equation:
x + (x + 2) + (x + 4) + (x + 6) = 296
Now let's solve this equation to find the value of x, which represents the first odd number.