Question

How many times does the digit 5 occur in all the numbers from 100-999 ?

Answer 1

It occurred 90 times

Step-by-step explanation:

Here, we want to know the number of times the digit occurs

We can solve this with arithemetic progression

The first term here is 105, while the last term is 995

However, the difference between each occurrence is 10

Thus, applying the formula:

`T_n\text{ = a + (n-1)d}`

Tn is the last term which is 995

a is the first term which is 105

d is the common difference which is 10

n is the number of terms which we want to calculate

Substituting these values, we have it that:

`\begin{gathered} 995\text{ = 105 + (n-1)10} \\ 995\text{ = 105 + 10n-10} \\ 995-105\text{ + 10 = 10n} \\ 10n\text{ = 900} \\ n\text{ =}(900)/(10) \\ n\text{ = 90} \end{gathered}`