Final answer:
The correct sigma notation for the series 3 + 6 + 12 + ... + 48 is Σ from n=1 to 16 of 3n, which matches option (a). This is because the term 48 corresponds to the 16th position in the series (3*16 = 48).
Step-by-step explanation:
The question requires expressing a given series in sigma notation. The series is 3 + 6 + 12 + ... + 48. Each term in this series can be obtained by multiplying the position of the term in the series by 3 (e.g., first term is 3, second term is 3*2, third term is 3*3, etc.). This indicates a pattern where each term can be represented as 3n, where 'n' is the position of the term in the series.
To express the series in sigma notation, we need to find the correct limits for 'n'. Given that the last term is 48, and using the pattern, we can determine that 48 is obtained when n is 16, since 3*16 = 48. Therefore, the sigma notation for this series would be the sum of 3n as n varies from 1 to 16, which is represented as:
Σn=116 3n
Option (a), (3n) from 1 to 16, is the correct answer.