Use the approach in Gauss's problem to find the sums of the arithmetic sequences below (do not use formulas).

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c. 3+ 6 + 9 + ... + 300

15150 is the required sum.

Step-by-step explanation:

Gauss method of summing sequences like this is to add the first term to the last term, the second term to the second to the last term and so on until you get to the middle. By doing this, you will always get the same sum. Then you divide the number of terms by two, because you are technically adding the first half of the sequence to the second half. You then multiply the sum of each pair that gave the same number with the number of terms that has been divided by 2. For this problem we have:

3 + 300 = 303

6 + 297 = 303

9 + 294 = 303

and so on.

100÷ 2 = 50.

Therefore we have 50 * 303 = 15150 is the required sum.