NSC / Matric Mathematics — practice by topic

1. Take any term of the sequence and look at how the next one is produced from it. 2. In an arithmetic sequence the same constant is added each time, and that constant is the common difference. 3. The constant may be negative, in which case the terms fall rather than rise. 4. Multiplying by a constant instead would build a geometric sequence. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 1: Sequences and series_

1. A geometric sequence grows or shrinks by the same factor at every step. 2. That factor is found by dividing any term by the term before it, and it is called the constant ratio. 3. So each new term is the previous term multiplied by that constant ratio. 4. Halving is only one special case of this, with a ratio of one half. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 1: Sequences and series_

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_