In an arithmetic progression the sum of the first n term,denoted by # S_n# is given by #S_n=n^2+8n# Find the first term and the common difference ?

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Answer 1 · 2018-04-20T05:39:45

The sum of the first n term of an AP,denoted by # S_n# is given by
#S_n=n^2+8n#

So

n th term of the series will be

#t_n=S_n-S_(n-1)=n^2+8n-((n-1)^2+8(n-1))#

#=>t_n=2n-1+8=2n+7#

Inserting #n=1,2,3....# we get

#"For "n=1tot_1=2*1+7=9#

#"For "n=2tot_2=2*2+7=11#

#"For "n=3tot_3=2*3+7=13#

Hence first term #t_1=9#
and common difference #d=t_2-t_1=11-9=2#

Check

Sum of first n terms

#S_n=n/2(2*9+(n-1)*2)#

#=>S_n=n/2(18+2n-2)#

#=>S_n=n/2(16+2n)#

#=>S_n=n^2+8n#