Answer:
There are 10 numbers between 1-100 which are equal to 5 times an odd number.
Explanation:
The odd numbers between 1 and 100 are 1,3,5,7…..
When these when these odd numbers are multiplied by 5 we get the following result.
[tex]5 \times 1=5[/tex]
[tex]5 \times 3=15[/tex]
[tex]5 \times 19=95[/tex]
These products form an AP 5,15,25,…..,95
common difference d=10
first term [tex]a=5[/tex]
last term [tex]a_n=95[/tex]
we have to calculate the number of terms n
The expression for last term [tex]a_n[/tex] of an AP is
[tex]a_n=a+(n-1)d[/tex]
[tex]a_n=a+nd-d[/tex]
[tex]nd=a_n-a+d =95-5+10=100[/tex]
[tex]n= \frac{100}{d}= \frac{100}{10}=10[/tex]
