Eggs over two years?

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1 Answer
Jim G.
Jan 20, 2018

#2806#

Explanation:

#"from Feb 2016 to Dec 2017"#

#"the sequence of eggs laid is"#

#75,79,83,87, ........#

#"these are the terms of an "color(blue)"arithmetic sequence"#

#a,a+d,a+2d,a+3d, ...... ,a+(n-1)d#

#"where a is the first term and d the common difference"#

#•color(white)(x)d=a_2-a_1=a_3-a_2= .... =a_n-a_(n-1)#

#"here "a=75,d=4" and "n=11+12=23#

#"the sum to n terms of an arithmetic sequence is"#

#•color(white)(x)S_n=n/2[2a+(n-1)d]#

#rArrS_(23)=23/2[(2xx75)+(22xx4)]=2737#

#"total number of eggs laid "=2737color(red)(+69)=2806#

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