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tamaranim1 [39]
3 years ago
7

Find the 7th term in the sequence with the following definition: a1 = 64 | 0

Mathematics
1 answer:
irinina [24]3 years ago
6 0

<u>Given:</u>

The first term of the sequence is a_1=64

The nth term of the sequence is a_n=\frac{a_{n-1}}{2}

We need to determine the 7th term of the sequence.

<u>Second term:</u>

Substituting n = 2 in the nth term of the sequence, we get;

a_2=\frac{a_{2-1}}{2}

a_2=\frac{a_{1}}{2}

a_2=\frac{64}{2}

a_2=32

Thus, the second term of the sequence is 32.

<u>Third term:</u>

Substituting n = 3 in the nth term of the sequence, we get;

a_3=\frac{a_{3-1}}{2}

a_3=\frac{32}{2}

a_3=16

Thus, the third term of the sequence is 16.

<u>Fourth term:</u>

Substituting n = 4 in the nth term of the sequence, we get;

a_4=\frac{a_{4-1}}{2}

a_4=\frac{16}{2}

a_4=8

Thus, the fourth term of the sequence is 8.

<u>Fifth term:</u>

Substituting n = 5 in the nth term of the sequence, we get;

a_5=\frac{a_{5-1}}{2}

a_5=\frac{8}{2}

a_5=4

Thus, the fifth term of the sequence is 4.

<u>Sixth term:</u>

Substituting n = 6 in the nth term of the sequence, we get;

a_6=\frac{a_{6-1}}{2}

a_6=\frac{4}{2}

a_6=2

Thus, the sixth term of the sequence is 2.

<u>Seventh term:</u>

Substituting n = 7 in the nth term of the sequence, we get;

a_7=\frac{a_{7-1}}{2}

a_7=\frac{2}{2}

a_7=1

Thus, the seventh term of the sequence is 1.

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Answer:

95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].

Step-by-step explanation:

We are given that in a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football.

Firstly, the pivotal quantity for 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is given by;

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where, \hat p = proportion of adults in the United States whose favorite sport to watch is football in a sample of 1219 adults = \frac{354}{1219}

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           p = population proportion of adults

<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5%

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P(-1.96 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 1.96) = 0.95

P( -1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } < {\hat p-p} < 1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } ) = 0.95

P( \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } < p < \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } ) = 0.95

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                         = [ \frac{354}{1219}-1.96 \times {\sqrt{\frac{\frac{354}{1219}(1-\frac{354}{1219})}{1219} } , \frac{354}{1219}+1.96 \times {\sqrt{\frac{\frac{354}{1219}(1-\frac{354}{1219})}{1219} } ]

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Therefore, 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].

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