Problem 59

Question

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

Step-by-Step Solution

Verified
Answer
The sum of the given arithmetic sequence is -25.
1Step 1: 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.
2Step 2: 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.
3Step 3: 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.