Question 949915
Let {{{n}}} = number of hours passed
You are summing:
{{{ 500 - 10n }}} for n = 1,2,3,4, ...
This numerical sequence = {{{ n*( n+1 )/2 }}}
For instance, say {{{ n = 5 }}}
{{{ 1 + 2 + 3 + 4 + 5 = 5*6/2 }}}
check it -it works
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Now I can say:
{{{ 3720 = 500n - 10*(n*(n+1)/2) }}}
{{{ 7440 = 1000n - 10*( n^2 + n ) }}}
{{{ 10n^2 + 10n - 1000n + 7440 = 0 }}}
{{{ 10n^2 - 990n + 7440 = 0 }}}
{{{ n^2 - 99n + 744 = 0 }}}
{{{ n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 1 }}}
{{{ b = -99 }}}
{{{ c = 744 }}}
{{{ n = (-(-99) +- sqrt( (-99)^2-4*1*744 ))/(2*1) }}}
{{{ n = ( 99 +- sqrt( 9801 - 2976 ))/ 2 }}}
{{{ n = ( 99 +- sqrt( 6825 ))/ 2 }}}
{{{ n = ( 99 - 82.6)/ 2 }}} ( makes sense to use -sqrt )
{{{ n = ( 99 - 83 )/2 }}} ( rounded off {{{82.6}}} )
{{{ n = 16/2 }}}
{{{ n = 8 }}}
check:
{{{ 500 + 490 + 480 + 470 + 460 + 450 + 440 + 430 = 3720 }}}
OK