Question

How many four digit numbers between 999 and 3000

Answer 1

2001

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Answer 2

In between the numbers 999 and 3000, there are totally 2000 four digit numbers.

Solution:

Four digits numbers between 999 and 3000 are:

1000, 1001, 1002 …………. 2999

The above series is arithmetic progression.

Hence, the first term (a) = 1000 …………… (1)

Common difference (d) = second term - first term = 1001-1000 = 1 ……….. (2)

and the nth term $\left(T_{n}\right)=2999 \ldots \ldots \ldots(3)$

According to formula,

n term of a A.P series $T_{n}=a+(n-1) d \ldots \ldots \ldots(4)$

By substituting the values of equations 1, 2, and 3 in equation 4,

We get,

$2999=1000+(n-1) \times 1$

$2999=1000+n-1$

$3000=1000+n$

n = 2000

Hence between 999 and 3000 there are 2000 four digits numbers.