GENERAL MATHEMATICS TERM 1 (2ND SUMMATIVE TEST LESSONS)

lessons include: patterns, sequence, series

pattern

predictable regularity

inspection

act of finding the rule of sequence

3 primary types of natural and artistic patterns

1. spiral and packing

2. concentric circles

3. tessellations

spiral and packing

nature packs elements tightly to maximize space

concentric circles

repeating waves outward

tessellations

tile-like repetitions of shapes with zero gaps

sequence

list of ordered numbers

fibonacci sequence

each number is the sum of two preceeding terms

leonardo pisano

experiment about how fast population of rabbit grows

common difference

adding or subtracting values

common ratio

multiplying or dividing the same value

formula for geometric sequence

a_n = a₁ (r )^n-1

formula for arithmetic sequence

a_n = a₁ + (n-1) d

formula of arithmetic series

S_n = n / 2 (a₁ + a_n) - with n

S_n = n / 2 [2a₁ + (n-1) d]

formula of geometric series

S_n = a₁ ( 1 - r ⁿ / 1 - r ) - with n

S_n = a₁ / 1 - r