find the sum of all natural number that are less than 100 and divisibal by 4
Answers
Answer:
Step-by-step explanation:
Answer:
The sum of all natural number that are less than 100 and divisible by 4 is 1200.
Step-by-step explanation:
List of all the numbers divisible by 4 and less than 100 is
4, 8 ,12, 16, 20, ............96.
Let the given list be of the form of an A.P.
Here,
first term (a) = 4,
common difference (d) = 8 - 4 = 4
Now let 'n' be the number of terms in the given A.P.
Therefore, nth term of AP = 96.
=> a+(n-1)d=96
=> 4+(n-1)4=96
=> (n-1)4=96-4
=> (n-1)=92/4
=> (n-1)=23
=> n=24
Hence, there are 24 terms in the AP.
So, Sum of first 24 terms = n/2[2×a+(n-1)d]
= 24/2[2×4+(24-1)4]
= 12(8+23×4)
= 12 × (8+92)
= 12 × 100
= 1200
Hence, the sum of all natural numbers divisible by 4 and less then 100 is 1200.
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