Home › NSC / Matric › Mathematics › Sequences and Series › Why can an arithmetic series never converge to a…
Why can an arithmetic series never converge to a finite sum?
AIts terms are always positive
BIts first term is always one
CIts sum runs off to infinity
DIts common difference is zero
Answer & Solution
Correct answer: C. Its sum runs off to infinity
1. A series converges when its running total settles closer and closer to one fixed value.
2. In an arithmetic sequence the terms never shrink towards zero, because the same constant is added each time.
3. Adding terms that do not shrink keeps pushing the total further out.
4. So the total heads off to positive or negative infinity and no limit exists.
5. Some geometric series do converge, because their terms can shrink towards zero.
_Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 1: Sequences and series_
Related questions
An arithmetic sequence has a first term of 7 and a common difference of 4. What is its fifA geometric series has a first term of 12 and a constant ratio of one third. What is its sIn a geometric sequence, how is each new term obtained from the term before it?What makes a sequence an arithmetic sequence?Sum of GP: 1 + 1/2 + 1/4 + ... to infinity =GP with first term 2, common ratio 3. Find 5th term.Sum of first 20 natural numbers:The 10th term of the AP 3, 7, 11, ... is: