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3 years ago

Find the 91st term of the arithmetic sequence 28, 8, -12, ...

Mathematics

1 answer:

lesya692 [45]3 years ago

3 0

Answer:

Step-by-step explanation:

The explicit formula for an arithmetic sequence is

$a_n=a_1+d(n-1)$

where n is the position of the number in the sequence, a1 is the first number in the sequence, and d is the common difference between the numbers.

If we are looking for the 91st term, our n = 91;

our a1 is 28, and

the common difference is -20. Putting all that together gives us the explicit formula for this sequence:

$a_{91}=28-20(91-1)$ and

$a_{91}=28-20(90)$ and

$a_{91}=28-1800$ so

$a_{91}=-1772$

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Answer:

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Step-by-step explanation:

a. 

Point estimate would be the proportion of the working people aged 65–69 to the sample size and equals $\frac{180}{600}=0.3$ ie 30%

b.

Let p be the proportion of people aged 65–69 who is working. OECD claims that percentage working had increased. Then null and alternative hypothesis would be

$H_{0}$ : p=27%

$H_{a}$ : p>27%

c.

z-score of the sample proportion assuming null hypothesis is:

$\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }$ where

p(s) is the sample proportion of working people aged 65–69 (0.3)
p is the proportion assumed under null hypothesis. (0.27)
N is the sample size (600)

then z= $\frac{0.3-0.27}{\sqrt{\frac{0.27*0.73}{600} } }$ = 1.655

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