Please helpPart 1.] Match these items.1.) The positive integers 2.) An ordering of quantities 3.) 2, 4, 8, 16, . . ., 256 4.) 1, 3, 5, 7, . . . 5.) No first term is available A.) An example of a finite sequenceB.) A sequenceC.) The reason the numbers . . . -4, -2, 0, 2, 4, . . . are not a sequenceD.) The natural numbersE.) An example of an infinite sequencePart 2.] Write the first five terms of the sequence. [tex] a_{n}= n^{2}+2[/tex]A.] 3,6,11,18,27B.] 3,6,9,12,15C.] 2,3,6,11,18Part 3.] Write the first five terms of the sequence. [tex] a_{n}= -1( \frac{1}{3})^{n-1}[/tex]A.] -1,-3,-9,-27,-81B.] -1,[tex] \frac{-1}{3},\frac{-1}{9},\frac{-1}{27},\frac{-1}{81} [/tex]C.] -1,[tex] \frac{1}{3},\frac{-1}{9},\frac{1}{27},\frac{-1}{81} [/tex]Part 4.] In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if it exists, and if possible find the sixth term. [tex]2a,2a^{2}b,2a^{3}b^{2},2a^{4}b^{3}...[/tex]
Accepted Solution
A:
Part 1 1) The positive integers -----------> D.) The natural numbers 2.) An ordering of quantities -----------> B.) A sequence 3.) 2, 4, 8, 16, . . ., 256 -----------> A.) An example of a finite sequence 4.) 1, 3, 5, 7, . . . -----------> E.) An example of an infinite sequence 5.) No first term is available -----------> C.) The reason the numbers . . . -4, -2, 0, 2, 4, . . . are not a sequence Part 2 [tex]a_n=n^2+2\\ a_1=1+2=3\\ a_2=4+2=6\\ a_3=9+2=11\\ a_4=16+2=18\\ a_5=25+2=27 [/tex] The answers is A. Part 3 [tex]a_n=-1(\frac{1}{3})^{n-1} \\ a_1=-1(\frac{1}{3})^{1-1}=-1\\ a_2=-1(\frac{1}{3})^{2-1}=-\frac{1}{3}\\ a_3=-1(\frac{1}{3})^{3-1}=--\frac{1}{9}\\ a_4=-1(\frac{1}{3})^{4-1}=--\frac{1}{27}\\ a_5=-1(\frac{1}{3})^{5-1}=--\frac{1}{81}\\ [/tex] The answers is B. Part 4 The pattern in this sequence is: [tex]a_n=2a^nb^{n-1}[/tex] Let's list first six terms: [tex]a_n=2a^nb^{n-1}\\
a_1=2a^1b^0=2a\\
a_2=2a^2b^1=2a^2b\\
a_3=2a^3b^2\\
a_4=2a^4b^3\\
a_5=2a^5b^4\\
a_6=2a^6b^5\\[/tex] This is a infinite sequence. The patern is obvious and we could find any term within the sequence.