9514 1404 393
Answer:
2a. 0.7, 0.3, -0.1, -0.5, -0.9
2b. 1, 3, 9, 27, 81
3a. geometric; r = 1/5
3b. arithmetic; d = -9
4. 234
5. 1/32
Step-by-step explanation:
2a. Start with the first term and add the common difference to get the next term.
0.7
0.7 -0.4 = 0.3
0.3 -0.4 = -0.1
-0.1 -0.4 = -0.5
-0.5 -0.4 = -0.9
The first 5 terms are 0.7, 0.3, -0.1, -0.5, -0.9.
__
2b. Start with the first term and multiply by the common ratio to get the next term.
The first 5 terms are 1, 3, 9, 27, 81.
__
3a. Obviously, the difference between 40 and 8 is not the same as the difference between 8 and 1.6. So, we look to see if the ratios are the same. They are:
8/40 = 1.6/8 = 1/5
This is a geometric sequence with a common ratio of 1/5.
__
3b. If the sign changes, but does not alternate, it cannot be a geometric sequence. The common difference is ...
-5 -4 = -14 -(-5) = -9
This is an arithmetic sequence with a common difference of -9.
__
4. Use n=50 and evaluate.
[tex]a_{50}=-11+5(50-1)=\boxed{234}[/tex]
__
5. Use n=7 and evaluate.
[tex]g_7=2\cdot\left(\dfrac{1}{2}\right)^{7-1}=\dfrac{2}{2^6}=\dfrac{1}{2^5}=\boxed{\dfrac{1}{32}}[/tex]
