Final answer:
The correct representation of the six-term arithmetic series starting with 10 and increasing by 2 each time is (a) (10 + 12 + 14 + 16 + 18 + 20).
Step-by-step explanation:
The student is asking about the arithmetic series for the given sequence (10 + 12 + 14 + ...) for six terms. An arithmetic series is a sequence of numbers with a common difference between consecutive terms. To determine which option correctly represents the six-term series, we have to add consecutive even numbers starting with 10, which has a common difference of 2.
Using the pattern, the series will be: 10 (first term) + 12 (second term) + 14 (third term) + 16 (fourth term) + 18 (fifth term) + 20 (sixth term). Hence, the correct answer is (a) (10 + 12 + 14 + 16 + 18 + 20).