Final answer:
To find the sum of an arithmetic series, use the formula S=(n/2)*(2a+(n-1)d). For the series 2+5+8+..., S7 is 147. For the series (-15)+(-10)+(5)+..., S6 is -10.
Step-by-step explanation:
To find the sum of an arithmetic series, we use the formula S = (n/2) * (2a + (n-1)d), where S is the sum, n is the number of terms, a is the first term, and d is the common difference.
1. In the series 2+5+8+..., the first term is 2, the common difference is 3, and we need to find S7. Plugging in these values into the formula, we get S = (7/2) * (2 + (7-1)*3) = 7*(2+18) = 7*20 = 140. Therefore, the correct answer is A. 147.
2. In the series (-15) + (-10) + (5) +..., the first term is -15, the common difference is 5, and we need to find S6. Plugging in these values into the formula, we get S = (6/2) * (-15 + (6-1)*5) = 3*(-15 + 25) = 3*10 = 30. Therefore, the correct answer is B. -10.