A partial sum of an arithmetic sequence is given. Find the sum.−7 + − 72 + 0 + 72 + 7 +    + 70

The given sequence is an arithmetic sequence, where each term increases by 72 from the previous term.

Step 1: Identify the first term (a) and the common difference (d) In this case, the first term a = -7 and the common difference d = 72.

Step 2: Identify the last term (l) The last term l = 70.

Step 3: Calculate the number of terms (n) The formula to calculate the nth term in an arithmetic sequence is: l = a + (n-1)*d. Rearranging the formula to solve for n gives: n = (l - a)/d + 1 = (70 - (-7))/72 + 1 = 77/72 + 1 ≈ 2.07. However, the number of terms in a sequence must be an integer, so we round up to the nearest whole number, n = 3.

Step 4: Calculate the sum of the sequence (S) The formula to calculate the sum of an arithmetic sequence is: S = n/2 * (a + l). Substituting the values gives: S = 3/2 * (-7 + 70) = 3/2 * 63 = 94.5.

Therefore, the sum of the given arithmetic sequence is 94.5.