Question 177700
you just set the equation to 300 and solve for n as follows:
n*(n+1)/2 = 300
(n^2 + n)/2 = 300
multiply both sides by 2 to get:
n^2 + n = 600
subtract 600 from both sides to get:
n^2 + n - 600 = 0
this is a quadratic equation.
factor to get:
(n+25) * (n-24) = 0
n = -25
or
n = 24
since n has to be positive, the only answer can be n = 24
substitute in original equation to get:
n * (n + 1)/2 = 300
which becomes:
(24*25)/2 = 300
which becomes:
600/2 = 300
which becomes:
300 = 300
equation is true so the value of n = 24 is good.
your answer is:
the number of consecutive integers, starting with 1, added together to get a sum of 300, is 24.
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