Problem: Write the first five terms of the geometric sequence defined by
a_{n }= 4(3^{n-1})
and find the sum of the first ten terms.
Solution (with communication): The first five terms are
4, 12, 36,108, and 324.
Using the TI-83, the sum of the first ten terms is
sum(seq(4*3^(x-1),x,1,10,1)) = 118,096. |
Problem: Identify a rule for the n-th term in the geometric sequence
-2, 8, -32, 128, -512, ...
and identify the term number for the sequence number
22463
Solution (with communication): We have a = -2 and r = -4. Hence, the n-th term is
a_{n} = -2(-4)^{n-1}.
The sequence consists only of even numbers. Hence the number 22463 is not a term in the sequence. |