Question
Are the given numbers form an $AP$? If they form an $AP$, write the next two terms: $1, -1, -3, -5, ...$
✓
Answer
From the given numbers, we have
$ a_2-a_1=-1-1=-2 $
$ a_3-a_2=-3-(-1)=-3+1=-2$
$ a_4-a_3=-5-(-3)=-5+3=-2$
$\text { i.e., } a_{k+1}-a_k $ is the same every time
So, the given list of numbers forms an $AP$ with the common difference $d = –2$
The next two terms are:
$-5 + (-2) = -7$ and
$-7 + (-2) = -9$
$ a_2-a_1=-1-1=-2 $
$ a_3-a_2=-3-(-1)=-3+1=-2$
$ a_4-a_3=-5-(-3)=-5+3=-2$
$\text { i.e., } a_{k+1}-a_k $ is the same every time
So, the given list of numbers forms an $AP$ with the common difference $d = –2$
The next two terms are:
$-5 + (-2) = -7$ and
$-7 + (-2) = -9$
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