10. Find the sum of all-natural numbers between 1605 and 1905 which are not divisible by 6.
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10. Find the sum of all-natural numbers between 1605 and 1905 which are not divisible by 6.
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Formulas:
sum of the arithmetic sequence
nth general term of the arithmetic sequence
where
a1 = first term
an = nth term
n = number of how many terms are
d = common difference
Analyze:
In the range from 1605 to 1905, the first number which is divisible by 6 is 1608 and the last number which is also divisible by 6 is 1902. The common difference is also 6. Before we get the sum where the numbers are divisible by 6, we need first to solve for n:
This means that there are 50 numbers which are divisible by 6 within that range.
So, the sum that are divisible by 6 is
Then, for the all-natural numbers, the common difference d = 1 because it is a counting integer. But we need to solve for n between 1605 and 1905.
So, the sum of all-natural numbers (including numbers that are divisible by 6) is
Because we need to find the sum of all-natural numbers which are not divisible by 6, we just subtract
Verified answer
Answer:
1905
Step-by-step explanation:
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