# For each of the following sequences: @ identify if the sequence is arithmetic, geometric or quadratic’. Justify your response. @ assuming the first item of each sequence is a1, give an expression for aj. (In other words, find a formula for the i-th term in the sequence). @ if the sequence is arithmetic or geometric, compute the sum of the first 10 terms in the sequence i 2,-12, 72, -432, 2592,... ii 9, 18, 31, 48, 69, 94,... iii 14, 11.5, 9, 6.5, 4, 1.5,... Question
Polynomial arithmetic For each of the following sequences: @ identify if the sequence is arithmetic, geometric or quadratic’. Justify your response. @ assuming the first item of each sequence is a1, give an expression for aj. (In other words, find a formula for the i-th term in the sequence). @ if the sequence is arithmetic or geometric, compute the sum of the first 10 terms in the sequence $$i 2,-12, 72, -432, 2592,...$$
$$ii 9, 18, 31, 48, 69, 94,...$$
$$iii 14, 11.5, 9, 6.5, 4, 1.5,...$$ 2020-12-18
Step 1 The series is $$2,−12,72,−432,2592,...$$ check the ratio $$\frac{-12}{2} = -6$$
$$\frac{72}{-12} = -6$$
$$\frac{-432}{72} = -6$$ this is geometrix series with common ratio r, where $$r = -6$$ the sequence is geometric (b) the general term $$a_i = a_1 r^(i-1)$$ where $$a_1$$ is the first term , r is the common ratio. substitute the values $$a_i = 2(−6)^(i−1)$$ hence, the expression for $$a_i is a_i = 2(−6)^{i -1}$$ Step 2 the sum of first 10 terms is given by the formula $$\frac{a(1-r^n)}{1- r}$$ substitute the values to get the sum of first 10 terms $$S_n = \frac{a(1-r^n)}{1- r}$$
$$= \frac{2(1-(-6)^n)}{1-(-6)}$$
$$= {2(1-(-6)^n)}{1+6}$$
$$= 17276050$$ hence, the sum of first 10 terms is given by 17276050

### Relevant Questions 1. Is the sequence $$0.3, 1.2, 2.1, 3, ...$$ arithmetic? If so find the common difference.
2. An arithmetic sequence has the first term $$a_{1} = -4$$ and common difference $$d = - \frac{4}{3}$$. What is the $$6^{th}$$ term?
3. Write a recursive formula for the arithmetic sequence $$-2, - \frac{7}{2}, -5, - \frac{13}{2} ...$$ and then find the $$22^{nd}$$ term.
4. Write an explicit formula for the arithmetic sequence $$15.6, 15, 14.4, 13.8, ...$$ and then find the $$32^{nd}$$ term.
5. Is the sequence $$- 2, - 1, - \frac{1}{2},- \frac{1}{4},...$$ geometric? If so find the common ratio. If not, explain why. In each of the​ following, list three terms that continue the arithmetic or geometric sequences. Identify the sequences as arithmetic or geometric. a. 2, 6, 18, 54, 162 b. 1, 8 ,15, 22, 29 c. 11, 15, 19, 23, 27 Consider the following sequence.
$$s_{n} = 2n − 1$$
(a) Find the first three terms of the sequence whose nth term is given.
$$s_{1} =$$
$$s_{2} =$$
$$s_{3} =$$
(b) Classify the sequence as arithmetic, geometric, both, or neither. arithmetic, geometric bothneither
If arithmetic, give d, if geometric, give r, if both, give d followed by r. (If both, enter your answers as a comma-separated list. If neither, enter NONE.) Consider the following sequence. $$\displaystyle{s}_{{n}}={2}{n}−{1}$$ (a) Find the first three terms of the sequence whose nth term is given. $$\displaystyle{s}_{{1}}={N}{S}{K}{s}_{{2}}={N}{S}{K}{s}_{{3}}=$$ (b) Classify the sequence as arithmetic, geometric, both, or neither. arithmeticgeometric bothneither If arithmetic, give d, if geometric, give r, if both, give d followed by r. (If both, enter your answers as a comma-separated list. If neither, enter NONE.) Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference, if it is geometric, find the common ratio. If the sequence is arithmetic or geometric,
find the sum of the first 50 terms.
$$\{9=\frac{10}{11}n\}$$
What type of sequence is $$\{9=\frac{10}{11}n\}? asked 2021-03-02 Write A if the sequence is arithmetic, G if it is geometric, H if it is harmonic, F if Fibonacci, and O if it is not one of the mentioned types. Show your Solution. a. \(\frac{1}{3}, \frac{2}{9}, \frac{3}{27}, \frac{4}{81}, ...$$ b. $$3, 8, 13, 18, ..., 48$$ An experiment on the probability is carried out, in which the sample space of the experiment is
$$S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.$$
Let event $$E={2, 3, 4, 5, 6, 7}, event$$
$$F={5, 6, 7, 8, 9}, event G={9, 10, 11, 12}, and event H={2, 3, 4}$$.
Assume that each outcome is equally likely. List the outcome s in For G.
Now find P( For G) by counting the number of outcomes in For G.
Determine P (For G ) using the General Addition Rule. Find the sum of the first n terms of the arithmetic sequence.$$−9 + (−12) + (−15)+ ... (to 10 terms)$$ Find the sum of the first 100 terms of an arithmetic sequence with 15th term of 86 and first term of 2. For Exercise, determine if the nth term of the sequence defines an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic, find the common difference d. If the sequence is geometric, find the common ratio r. $$a_{n} = 5 \pm \sqrt{2n}$$ Iron is very important for babies' growth. A common belief is that breastfeeding will help the baby to get more iron than formula feeding. To justify the belief, a study followed 2 groups of babies from born to 6 months. With one group babies are breast fed, and the other group are formula fed without iron supplements. Data below shows iron levels of those two groups of babies. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{G}{r}{o}{u}{p}&{S}{a}\mp\le\ {s}{i}{z}{e}&{m}{e}{a}{n}&{S}{\tan{{d}}}{a}{r}{d}\ {d}{e}{v}{i}{a}{t}{i}{o}{n}\backslash{h}{l}\in{e}{B}{r}{e}\ast-{f}{e}{d}&{23}&{13.3}&{1.7}\backslash{h}{l}\in{e}{F}{\quad\text{or}\quad}\mu{l}{a}-{f}{e}{d}&{23}&{12.4}&{1.8}\backslash{h}{l}\in{e}{D}{I}{F}{F}={B}{r}{e}\ast-{F}{\quad\text{or}\quad}\mu{l}{a}&{23}&{0.9}&{1.4}\backslash{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ (1) There are two groups we need to compare for the study: Breast-Fed and Formula- Fed. Are those two groups dependent or independent? Based on your answer, what inference procedure should we apply for this research? (2) Please perform the inference you decided in (1), and make sure to follow the 5-step procedure for any hypothesis test. (3) Based on your conclusion in (2), what kind of error could you make? Explain the type of error using the context words for this research