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Chapter 9: Problem 59

Find the sum of the finite arithmetic sequence. $$-1+(-3)+(-5)+(-7)+(-9)$$

Short Answer

Expert verified
The sum of the given arithmetic sequence is -25.

Step by step solution

01

Identify the first term, common difference and the last term

In this case, the first term (a) is -1, the common difference (d) is -2 (since each subsequent term is 2 units less than the previous term), and the last term (l) is -9.
02

Identify the number of terms (n)

We can find the number of terms in this arithmetic sequence by using the formula 'l = a + (n-1)*d'. By substituting the values which found previously into the formula, we get: n= ((l-a)/d) + 1 = ((-9 - (-1))/-2) + 1 = 5.
03

compute the sum of the sequence (Sn)

Now we can compute the sum of this arithmetic sequence using the formula: Sn = n/2 * (a + l). This would become Sn = 5/2 * (-1 -9) = -25.

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