Question

1. use the following to determine the sum. 123,121, 119, ..., -51

Explanation:

Step1: Identify sequence parameters

This is an arithmetic sequence with first term $a_1=123$, common difference $d=121-123=-2$, last term $a_n=-51$.

Step2: Find number of terms $n$

Use arithmetic sequence formula $a_n = a_1 + (n-1)d$
$$-51 = 123 + (n-1)(-2)$$
$$-51 - 123 = -2(n-1)$$
$$-174 = -2(n-1)$$
$$n-1 = \frac{-174}{-2}=87$$
$$n=87+1=88$$

Step3: Calculate sum of the sequence

Use arithmetic series sum formula $S_n = \frac{n}{2}(a_1 + a_n)$
$$S_{88} = \frac{88}{2}(123 + (-51))$$
$$S_{88}=44\times72$$

Answer:

3168