Question
Find how many three digit natural numbers are divisible by 5.
✓
Answer
List of three digit number divisible by 5 are
100, 105,110,115,……….. 995
Let us find how many such number are there?
From the above sequence, we know that
$t_n=995, a=100$
$t_1=105, t_2=110$
Thus, $d=t_2-t_1=110-105=5$
Now, By using $n^{\text {th }}$ term of an A.P. formula
$t_n=a+(n-1) d$
we can find value of " $n$ "
Thus, on substituting all the value in formula we get
$995=100+(n-1) \times 5$
$\Rightarrow 995-100=(n-1) \times 5$
$\Rightarrow 895=(n-1) \times 5$
$\Rightarrow n -1=\frac{895}{5}=179$
$\Rightarrow n=179+1=180$
100, 105,110,115,……….. 995
Let us find how many such number are there?
From the above sequence, we know that
$t_n=995, a=100$
$t_1=105, t_2=110$
Thus, $d=t_2-t_1=110-105=5$
Now, By using $n^{\text {th }}$ term of an A.P. formula
$t_n=a+(n-1) d$
we can find value of " $n$ "
Thus, on substituting all the value in formula we get
$995=100+(n-1) \times 5$
$\Rightarrow 995-100=(n-1) \times 5$
$\Rightarrow 895=(n-1) \times 5$
$\Rightarrow n -1=\frac{895}{5}=179$
$\Rightarrow n=179+1=180$
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