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Alexxx [7]
3 years ago
15

The 8th term in the arithmetic sequence is 17, the 12th term is 25. Find the first term, and the sum of the first 20 terms.

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

Answer:

First term a = 3

Sum of first 20 term = 440

Step-by-step explanation:

Given:

8th term of AP = 17

12th term of AP = 25

Find:

First term a

Sum of first 20 term

Computation:

8th term of AP = 17

a + 7d = 17 ....... EQ1

12th term of AP = 25

a + 11d = 25 ...... EQ2

From EQ1 and EQ2

4d = 8

d = 2

a + 7d = 17

a + 7(2) = 17

First term a = 3

Sum of first 20 term

Sn = [n/2][2a + (n-1)d]

S20 = [20/2][(2)(3) + (20-1)2]

S20 = [10][(6) + 38]

S20 = [10][44]

S20 = 440

Sum of first 20 term = 440

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Step-by-step explanation:

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The confidence interval for the mean is given by the following formula:

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And for the margin of error we have the following estimation:

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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75

And for the margin of error we have the following estimation:

ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62

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