Question 205056

The largest number in the sequence is calculated as: {{{(2L+L^2)/2=121524}}}, or: {{{L^2+2L-243048=0}}}, which is then calculated using the quadratic equation formula, {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}, and with a = 1, b = 2, and c = - 243,048


The largest number in the sequence is 492, and that makes the average of the numbers in the sequence 247 (mean or average of the largest and smallest values in the sequence), or, {{{(2+492)/2}}}


Therefore, the number of numbers in the sequence is {{{highlight_green(246)}}}, 

calculated as: {{{(492 - 2 + 2)/2}}}


Check:

Sum of numbers in sequence = average of largest and smallest values, times the number of numbers in the sequence, or, {{{247*246}}} = 60,762. To put it another way, number of numbers in a sequence = Sum of the numbers in the sequence, divided by the average, or mean of the numbers in the sequence, or, 

{{{60762/247=246}}} numbers