Question
Is the given series: $0, -4, -8, -12, ....$forms an $AP?$ If it forms an $AP$, then find the common difference $d$ and write three more terms.
✓
Answer
Here: $a_2-a_1=-4-0=-4$
$a_3-a_2=-8+4=-4$
$a_4-a_3=-12+8=-4$, since $a_{k+1}-a_k$ is same for all values of k
Hence, this is an $AP$.
The next three terms can be calculated as follows:
$a_5=a+4 d=0+4(-4)=-16 $
$ a_6=a+5 d=0+5(-4)=-20 $
$ a_7=a+6 d=0+6(-4)=-24$
Thus, the next three terms are: $-16, -20$ and $-24$
$a_3-a_2=-8+4=-4$
$a_4-a_3=-12+8=-4$, since $a_{k+1}-a_k$ is same for all values of k
Hence, this is an $AP$.
The next three terms can be calculated as follows:
$a_5=a+4 d=0+4(-4)=-16 $
$ a_6=a+5 d=0+5(-4)=-20 $
$ a_7=a+6 d=0+6(-4)=-24$
Thus, the next three terms are: $-16, -20$ and $-24$
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