Question

1. (0 points) find the sum of the first 78 terms of the arithmetic sequence with first term (a_1 = -18) and common difference (d = 2).

Explanation:

Step1: Identify given values

$$n = 78, \quad a_1 = -18, \quad d = 2$$

Step2: State the sum formula

$$S_n = \frac{n}{2} [2a_1 + (n - 1)d]$$

Step3: Substitute the values

$$S_{78} = \frac{78}{2} [2(-18) + (78 - 1)2]$$

Step4: Simplify inside brackets

$$S_{78} = 39 [-36 + 77 \times 2]$$

Step5: Calculate the sum

$$S_{78} = 39 [-36 + 154] = 39 \times 118 = 4524$$

Answer:

4524