Can you think of any other kinds of sequences? List out five different types of sequences and discuss their properties with your friends.                                                                                                                                              [Page No. 176]

There are many kinds of sequences. Here are five different types, each with a property that describes it.

1. Even numbers

2, 4, 6, 8, 10, ... : increasing, with a constant difference of 2 between terms (an arithmetic progression).

2. Powers of 2

1, 2, 4, 8, 16, 32, ... : each term is twice the previous one, so it grows by multiplying by a fixed number (a geometric progression).

3. Unit fractions

1, $\frac{1}{2}$, $\frac{1}{3}$, ... : the terms decrease and get closer and closer to 0, but never become negative.

4. Negative integers

-1, -2, -3, -4, ... : a decreasing sequence with a constant difference of -1; the terms are all negative.

5. Cube numbers

1, 8, 27, 64, 125, ... : each term is $n^3$; the terms increase, but neither the difference nor the ratio between terms is constant.

Other interesting examples include the Viraňanka-Fibonacci sequence 1, 2, 3, 5, 8, 13, ... (each term is the sum of the previous two) and the prime numbers 2, 3, 5, 7, 11, ... (which follow no simple rule).