What is the sum of all natural numbers from 1 to 1000 that are divisible by 7
(1) 61061
(2) 71271
(3) 71071
(4) 73371
market value was Rs. 120. CO
Answers
Answer:
(3) 71071
Step-by-step explanation:
To find ---> Sum of all natural numbers
from 1 to 1000 that are divisible by 7.
Solution---> First natural number which
is divisible by 7 starting from 1 is 7 and
then 14 , 21 , 28 .......... and last natural
number which is divisible by 7 up to
1000 is 994
So natural numbers which are divisible by 7 from 1 to 1000 are
7,14,21,28,.......................,994
these natural numbers formed an AP
Now we first find that which term of AP is 994
a = 7 , d = 14 - 7 =7 , aₙ = 994 , n = ?
aₙ = a + ( n - 1 ) d
=> 994 = 7 + ( n - 1 ) 7
=> 994 - 7 = ( n - 1 ) 7
=> 987 = ( n - 1 ) 7
=> 987 / 7 = n - 1
=> 141 = n - 1
=> n = 141 + 1
=> n = 142
It means natural numbers from 1 to
1000 which are divisible by 7 is 142
Now we calculate sum of these terms
a = 7 , d = 7 , n = 142 , Sₙ = ?
Sₙ = n/2 { 2a + ( n - 1 ) d }
= 142 / 2 { 2 ( 7 ) + ( 142 - 1 ) 7 }
= 71 { 14 + ( 141 ) 7 }
= 71 ( 14 + 987 )
= 71 ( 1001 )
= 71071
option 3)71071
#answerwithquality #bal