Math 1 · Unit 9 · Lesson 1 · part 3 of 5
A sequence is a function made of dots
A sequence is a list of numbers in a set order.
A sequence is a function made of dots
A sequence is a list of numbers in a set order. Each number in the list is a term. Every term has a place in line, its term number (also called its position or index): first, second, third.
A theater has 60 seats in row 1, 68 seats in row 2, 76 seats in row 3, and keeps going the same way.
| row (the term number) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| seats (the term) | 60 | 68 | 76 | 84 | 92 |
Look at that table the Unit 2 way. A number goes in (the row), and exactly one number comes out (the seats in that row). That is a function: the term number is the input, and the term is the output. Row 3 never has two different seat counts, so it passes the function test.
Watch the terms appear one at a time. Each one is plotted as a dot, and nothing is drawn between the dots.
The notation. Writing "the term in position 4" gets long, so there is a short way. The letter a stands for a term, and a small number written low, a subscript, says which one.
a1, said "a sub 1"
The first term. In the theater, a1 = 60.
a4, said "a sub 4"
The fourth term. In the theater, a4 = 84.
an, said "a sub n"
The nth term: the term in position n, whichever n you choose.
f(n), function notation
The same thing, written the Unit 2 way. f(4) = 84 and a4 = 84 say exactly the same sentence: row 4 has 84 seats.
The subscript is a label, not a multiplication and not an exponent. a4 does not mean a times 4.