Question

Identify the following series as arithmetic, geometric, both, or neither.

-0
-Σ(3 + na)
-n=1
-both
-arithmetic
-geometric
-neither

Answer 1

The series - ∑(3 + na) is an arithmetic series because it exhibits a constant difference 'a' between successive terms.

Step-by-step explanation:

The student's question asks to identify whether the series represented by - ∑(3 + na), where the sum is over 'n' from 1 to infinity, is arithmetic, geometric, both, or neither. An arithmetic series has a common difference between terms, while a geometric series has a common ratio between terms. In the given series, each term increases by a constant 'a' from the previous term, indicating a common difference. Thus, the series is arithmetic because it can be expressed as a sequence where each term after the first is obtained by adding a fixed number to the previous term.