Calculate the sum of all natural numbers from 100 to 200 both inclusive which are not divisible by 6
First we'll find the sum of all natural numbers from 100 to 200, inclusive.
Then we'll find the sum of all the multiples of 6 from 102 to 198, inclusive.
Then we'll subtract them.
All natural numbers from 100 to 200, inclusive.
That's the arithmetic sequence 100,101,102,103,...,200
with a1=100, d=1, and an=200
an = a1 + (n-1)d
To find the number of terms:
200 = 100 + (n-1)1
100 = n-1
101 = n
We use the sum formula
Sn = (a1 + an)
S101 = (100 + 200) = = 15150
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The multiples of 6 from 102 to 198, inclusive, is the arithmetic
sequence 102,108,114,...,198, with a1=100, d=1, and an=200
To find the number of terms:
an = a1 + (n-1)d
198 = 102 + (n-1)6
198 = 102+6n-6
198 = 96+6n
102 = 6n
17 = n
We use the sum formula
Sn = (a1 + an)
S7 = (102 + 198) = = 2550
Subtracting, 15150-2550 = 12600.
Answer = 12600.
Edwin