1. Do all sequences have patterns?
No, many sequences can have no pattern at all. e.g. 3, 100, 32, 8
2. What is the relationship between sequences and the natural numbers 1, 2, 3, 4...?
Because the first term relates to the first natural number, 1
the second term relates to the second natural number, 2 etc.
3. What do the two numbers at the top and bottom of the sigma sign mean?
These are the values the variable takes on. The variables after the sigma sign take on all INTEGER values from the lowest one at bottom of the sigma sign to the highest one at the top of the sigma sign
e.g.
. means put n = 1, then n = 2, then n = 3, then n = 4 and finally n = 5 into the expression 3 n. i.e. Each integer between 1 and 5.
4. What is the difference between a sequence and a series?
A sequence is an ordered set of numbers which is determined by a rule.
A series is a sum of successive members of a sequence.
