How do you find the first three terms of the arithmetic series #a_1=-13#, #a_n=427#, #S_n=18,423#?

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Answer 1 · 2016-10-20T09:57:36

First three terms of arithmetic series are #-13#, #-8# and #-3#

In the arithmetic series whose first term is #a_1# and common difference is #d#

#n^(th)# term is #a_n=a_1+(n-1)d#

and #S_n#, the sum of first #n# terms is given by

#S_n=n/2(a_1+a_n)#

as here, we have #a_1=-13#, #a_n=427# and #S_n=18423#

#18423=n/2(-13+427)#

or #n/2=18423/(427-13)=18423/414=(89xx207)/(2xx207)=89/2#

and #n=89#

as #a_n=a_1+(n-1)d#, we have #427=-13+(89-1)d#

or #88d=427+13=440# i.e. #d=5#

and first three terms are #-13#, #-13+5=-8# and #-8+5=-3#.