Question

Find the sum of all natural numbers between 1000and 10000

Answer 1

The sum of all natural numbers from 1000 and 10000 is 49505500.

• All natural numbers form a series of AP with common difference(d) as 1.
• We have to find the sum of all natural numbers from 1000 and 10000.
• Here the first term of the AP will be 1000 and the last term of the AP will be 10000.
• Sum of AP where the first term and last term is known is given by

Sum of AP = $\frac{n}{2} [first \ term + last \ term]$

where n is the number of terms in the sequence.

• to find the number of terms in the AP we know the last term, we  use the formula of last term as

$t_n = a + (n-1) d$ , where $t_n$ denotes last term , a denotes first term and n stands for number of terms.

10000 = 1000 + (n-1) × 1

9000 = n - 1

n = 9001

• Sum of the series will be equal to

Sum = $\frac{9001}{2} [1000 + 10000]$

Sum = $\frac{9001}{2} [11000]$

Sum = 9001 × 5500

Sum = 49505500