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AlekseyPX
2 years ago
15

Find the first four terms of the sequence given by the following. aₙ=43-3(n-1) n=1,2,3. . .

Mathematics
1 answer:
Serggg [28]2 years ago
7 0

Given :-

  • The general term of a sequence is given by aₙ=43-3(n-1) .

To Find :-

  • The first four terms of the sequence.

Solution :-

The given expression is /

→ aₙ=43-3(n-1)

where n > 0

<u>Finding</u><u> the</u><u> </u><u>first </u><u>term </u><u>:</u>

Substituting n = 1 , we have ,

→ T1 = 43 - 3(1-1)

→ T1 = 43 - 3*0

→ T1 = 43 - 0 = 43

<u>Finding</u><u> the</u><u> </u><u>second</u><u> </u><u>term </u><u>:</u>

Substituting n = 2 , we have,

→ T2 = 43 -3(2-1)

→ T2 = 43 -3*1

→ T2 = 43 -3 = 40

<u>Finding</u><u> </u><u>the </u><u>third </u><u>term</u><u> </u><u>:</u>

Substituting n = 3 , we have,

→ T3 = 43 -3(3-1)

→ T3 = 43 -3*2

→ T3 = 43 -6 = 37

<u>Finding</u><u> the</u><u> </u><u>fourth</u><u> </u><u>term </u><u>:</u>

→ T4 = 43 -3(4-1)

→ T4 = 43 -3*3

→ T4 = 43-9 = 34

<u>Hence</u><u> the</u><u> </u><u>first</u><u> </u><u>four</u><u> terms</u><u> of</u><u> </u><u>the</u><u> </u><u>sequence</u><u> </u><u>are </u><u>4</u><u>3</u><u> </u><u>,</u><u> </u><u>4</u><u>0</u><u> </u><u>,</u><u> </u><u>37</u><u> </u><u>and </u><u>34</u><u> </u><u>.</u>

<em>I </em><em>hope</em><em> this</em><em> helps</em><em> </em><em>.</em><em> </em><em>Let </em><em>me</em><em> know</em><em> if</em><em> you</em><em> </em><em>need </em><em>further</em><em> </em><em>clarification</em><em> </em><em>.</em>

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\alpha=0.05 represent the significance level for the hypothesis test.  

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We need to conduct a hypothesis in order to check if the true mean for vacation days is higher than 15, the system of hypothesis would be:  

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Alternative hypothesis:\mu > 15  

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