The first term of an arithmetic sequence is 10 and its common difference is -3. What is the sum of the first
10 terms of this sequence?

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The sum of the first ten terms is -35.

Step-by-step explanation:

The first term of an arithmetic sequence is 10, and its common difference is -3.

We want to find the sum of the first 10 terms of this sequence.

Remember that the sum for an arithmetic sequence is given by:

Where k is the number of terms, a is the initial/first term, and x_k is the last term.

Since our initial term is 10, a = 10.

And since we want to find the sum of the first ten terms, k = 10.

So, we will need to find the last or tenth term. We can write an explicit formula. The standard explicit formula for an arithmetic sequence is:

Where a is the initial term and d is the common difference.

So, by substituting, we acquire:

Then the tenth or last term is:

Then the sum of the first ten terms will be:  

-35

Step-by-step explanation:

= 10+(-3)(0) = 10

= 10+(-3)(9) = -17

= 10[(10 -17)/2] = 10(-7/2) = -70/2