Find the common difference of the A.P. and write the next two ter… - Vidyadip

Question

Find the common difference of the A.P. and write the next two terms:
$75,67,59,51, \ldots . .$

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Answer

Given,
$75,67,59,51, \ldots . .$
Here, $a_1-75, a_2=67, a_3=59, a_4=51$
Difference between terms
$d_1=a_2-a_1=67-75=-8$
$d_2=a_3-a_2=59-67=-8$
$\text { and } d_3=a_4-a_3=51-59=-8$
So, common difference is $-8$
Now, next two terms:
$a_n=a_{n-1}+d$
$5^{\text {th }} \text { term }$
$a_5=a_{5-1}+(-8)$
$=a_4-8$
$=51-8$
$\Rightarrow a_5=43$
$6^{\text {th }} \text { terms, }$
$a_6=a_{6-1}+(-8)$
$=a_5-8$
$=43-8$
$\Rightarrow a_6=35$
Hence, common differnce is $-8$ and next two terms $43$ and $35$ .

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