Find the common difference and write the next four terms of the f… - Vidyadip

Question

Find the common difference and write the next four terms of the following arithmetic progressions:
$0, -3, -6, -9, .....$

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Answer

Here, first term $\left(a_1\right)=0$
Common difference $(d)=a_2-a_1$
$ =-3-0 $
$ =-3$
Now, we need to find the next four terms of the given A.P.
That is we need to find $a_5, a_6, a_7, a_8$
So, using the formula $a_n=a+(n-1) d$
Substituting $\mathrm{n}=5,6,7,8$ in the above formula
Substituting $\mathrm{n}=5$, we get
$a_5=0+(5-1)(-3) $
$ a_5=0-12 $
$ a_5=-12$
Substituting $n=6$, we get
$ a_6=0+(6-1)(-3) $
$ a_6=0-15 $
$ a_6=-15$
Substituting $\mathrm{n}=7$, we get
$ a_7=0+(7-1)(-3) $
$ a_7=0-18 $
$ a_7=-18$
Substituting $n=8$, we get
$a_8=0+(8-1)(-3) $
$ a_8=0-21 $
$ a_8=-21$
Therefore, the common difference is $d = -3$ and the next four terms are $-12, -15, -18, -21.$

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