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2 years ago

Find the thirty-second term of the following sequence. 9, 15, 21, ... 186 199 195

2 answers:

5 0

The question can be answered using the arithmetic sequence formula: an<span> = a</span>1<span> + (n – 1)d.
d = 6
a1 = 9
n = 32
an = ?

an = 9 + (32-1)6
an = 9 + 31x6
an = 195

so, the 35th term is 195</span>

SVETLANKA909090 [29]2 years ago

4 0

<h2>Answer:</h2>

The thirty-second term of the sequence is:

195

<h2>Step-by-step explanation:</h2>

We are given a sequence as:

9,15, 21, .....

The first term of the sequence is:

$a_1=a=9$

Also, we could observe that the sequence has a common difference(d) : 6

Since,

15-9=6

21-15=6

This means that the sequence is an arithmetic sequence with:

$a=9\ and\ d=6$

Also, we know that the nth term of a sequence is given by the formula:

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

Hence,

$a_{32}=9+(32-1)\times 6\\\\\\a_{32}=9+31\times 6\\\\\\a_{32}=9+186\\\\\\a_{32}=195$

Hence, the answer is:

195

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Note: This question is incomplete and complete question is posted down below with multiple choice questions and from Option 3 is correct

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Note: This question is incomplete and it is a multiple choice question. With the following multiple choices to select from.

1. The researchers expect that 80% of all similarly constructed intervals will contain the true mean number of oocytes that could be retrieved from the population of women aged 36-40 years.

2. The researchers expect that 80% of all similarly constructed intervals will contain the mean number of oocytes retrieved in the sample of 98 women aged 36-40 years.

3. There is a 80% chance that the the true mean number of oocytes that could be retrieved from the population of women aged 36-40 years is uniquely contained in the reported interval.

4. The researchers expect that 80% of all similarly constructed intervals will contain the range of the number of oocytes that could be retrieved from the population of women aged 36-40 years.

we have to select the appropriate answer from the above options.

So, in order to choose the correct option, first we need to understand the confidence interval.

Confidence Interval is a range of value for which are pretty sure our true values will lie in that interval. For example, in this question, we have 80% confidence interval and it means there is a 80% confident chance that our true values will lie in that 80% interval. Let's calculate it.

We have following data given from the question.

Sample = 98

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And formula for confidence interval is :

Mean ± Z x SD/ $\sqrt{n}$

For this equation, we have all quantities except SD which is standard deviation. Let's calculate it first.

Standard deviation is square root of variance and so we need to calculate variance first.

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s² = (950.6 (1 - 9.7)²) ÷ (98-1)

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Let's calculate Standard deviation

SD = $\sqrt{variance}$

SD = $\sqrt{741.762}$

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Now, we have complete data to calculate range of values for the confidence interval of 80%

Mean ± Z x SD/ $\sqrt{n}$

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