Question

FIND THE SUM OF ALL NATURAL NUMBERS BETWEEN 1000 AND 10000?

Answer 1

The list of natural numbers between 1000 and 10000 is :1001, 1002, ....9999

a = 1001
d = 1
an = 9999

⇒a+(n−1)d = 9999
⇒1001 + n−1 = 9999
⇒n+1000 = 9999
⇒n = 8999
Sn = n/22a+(n−1)d]
⇒S8999 = 8999/2[2×1001+8998]
⇒S8999 =8999/2[11000]
⇒S8999 =8999×5500
⇒S8999 =49,494,500

Answer 2

s=n/2[2a+(n-1)d]
a=1001
d=1
n=8999
s=49494500