In an AP, $Sn=3n+5$,then the valve of $d$ is______.

Given:

In an AP, $Sn=3n+5$

To do:

We have to find the value of $d$.
Solution:

Let the first time be $a$ and common difference be $d$.

This implies,

$S_1=3(1)+5$

$=3+5$

$=8$

$\Rightarrow a_1=a=8$

$S_2=3(2)+5$

$=6+5$

$=11$

$\Rightarrow a_1+a_2=11$

Therefore,

$8+a_2=11$

$a_2=11-8$

$=3$

$\Rightarrow d=a_2-a_1=3-8$

$=-5$

The value of $d$ is $-5$.

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Updated on: 10-Oct-2022

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