Finite and Infinite Geometric Sequence The sequence is said to be Finite if the last term or the number of terms is known,
while the sequence is said to be Infinite if the last term or the number of terms is
unknown Observe the given sequences below.
A
B
с
1, 0.1, 0.01, 0.001
16, 32, 64, 128, 256
3, 9, 27, 81, 243
10, 20, 40, 80, 160
9604, 1372, 196, 28, 4
1, 0.1, 0.01, 0.001
9604, 1372, 196, 28, 4,
256, 128, 64, 32, 16,
243, 81, 27, 9, 3,...
160, 80, 40, 20, 10,
16, 32, 64, 128, 256,
3,9, 27, 81, 243,
10, 20, 40, 80, 160
0.001, 0.01, 0.1, 1,-
4, 28, 196, 1372, 9604,
Can you determine the difference between these two sequences?
1, 0.1, 0.01, 0.001 and 1, 0.1, 0.01, 0.001,
16, 32, 64, 128, 256 and 16, 32, 64, 128, 256,
3,9, 27, 81, 243 and 3, 9, 27, 81, 243,
Which sequences are finite and which sequences are infinite?
Give the value of the common ratio
of
each sequence by dividing any term by
the preceding term. Is |r| < 1?
1, 0.1, 0.01, 0.001, ...
9604, 1372, 196, 28, 4, ...
256, 128, 64, 32, 16, ...
243, 81, 27, 9, 3, ...
160, 80, 40, 20, 10,
Give the value of the common ratio of
each sequence by dividing any term
by the preceding term. Is lr| > 1?
16, 32, 64, 128, 256,
3,9, 27, 81, 243, ...
10, 20, 40, 80, 160,
→ 0.001, 0.01, 0.1, 1, ...
4, 28, 196, 1372, 9604
Can you now determine how sequences were grouped?
If you were to get the sum of the terms of an infinite geometric sequence, which
sum converges? Diverges?