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

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

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

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

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

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