Sequences & Series

Sequences and Series Revision Points

Understand the difference between arithmetic sequences and geometric sequences.
Recognise fibonacci sequences and understand the principle behind their creation.
Know the difference between finite sequences and infinite sequences.

Determine the nth term of both arithmetic and geometric sequences.
Identify the ‘common difference’ in an arithmetic sequence and the ‘common ratio’ in a geometric sequence.
Understand the concept of an individual sequence term as well as the initial term.

Understand how to calculate the sum of an arithmetic series using the formula S_n = n/2(2a + (n-1)d), where ‘a’ is the first term, ‘n’ is the number of terms, and ‘d’ is the common difference.
Be able to apply the formula for the sum of a geometric series: S_n = a(r^n - 1) / (r - 1) where ‘a’ is the first term, ‘r’ is the common ratio, and ‘n’ is the number of terms.
Comprehend the concept of the sum to infinity of a decreasing geometric series where r < 1.

Appreciate the real-world application of arithmetic and geometric sequences and series, such as in financial mathematics or population projection.
Understand how to interpret problem situations involving sequences and series, such as pay-off terms for loans or total distances in repetitive spatial patterns.
Apply the knowledge of sequences and series to solve word problems.