Final answer:
To find the value of the arithmetic series, the common difference is calculated as -8, and the sum formula for an arithmetic series is used to determine the series total.
Step-by-step explanation:
To determine the value of the arithmetic series given in the question, we first need to identify the common difference (d). By looking at the first few terms of the series: 14, 14 + 6(-2) = 2, and 2 + (-10) = -8, we can see that the common difference is -8 (since 2 - 14 = -12 and -8 - 2 = -10, it confirms a pattern of adding -12). To find the sum of the series, we can use the sum formula for an arithmetic series: Sn = n/2 (a1 + an), where n is the number of terms, a1 is the first term, and an is the last term.
To find n, let's set up the formula for the nth term of the arithmetic series: an = a1 + (n - 1)d. Substituting the known values: -154 = 14 + (n - 1)(-12) gives us n. Once we determine n, we can then plug the values back into the sum formula to find the value of the arithmetic series.