Final answer:
The expanded form of the series S_5 is calculated by plugging in values of k from 1 to 5 into the given expression. The resulting terms are -3, 2, 7, 12, and 17, making the expanded form -3 + 2 + 7 + 12 + 17.
Step-by-step explanation:
The expanded form of the series S_5 = ∑_{k=1}^5[-3+(k-1)5] involves computing each term of the series for values of k from 1 to 5. To find the first term, we substitute k=1 into the expression to get -3 + (1-1)5 which simplifies to -3. Continuing this process for k=2, k=3, k=4, and k=5, we get subsequent terms of 2, 7, 12, and 17 respectively.
The given series is represented as: S5 = ∑k=15 [-3 + (k-1)5].
To find the expanded form of the series, we substitute the values of k from 1 to 5 into the expression.
Expanding the expression gives us:
-3 + (1-1)5 = -3 + 0 = -3
-3 + (2-1)5 = -3 + 5 = 2
-3 + (3-1)5 = -3 + 10 = 7
-3 + (4-1)5 = -3 + 15 = 12
-3 + (5-1)5 = -3 + 20 = 17
Therefore, the expanded form of the series is: -3 + 2 + 7 + 12 + 17.
Therefore, the expanded form of the series is -3 + 2 + 7 + 12 + 17, which corresponds to choice A.