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lawyer [7]
3 years ago
11

In an arithmetic​ sequence, the nth term an is given by the formula an=a1+(n−1)d​, where a1 is the first term and d is the commo

n difference.​ Similarly, in a geometric​ sequence, the nth term is given by 1an=a1•rn−1​,
where r is the common ratio. Use these formulas to determine

the indicated term in the given sequence.

The 105th term of 1/2, 1, 3/2, 2,..
Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
7 0

Answer:

105th term of given series is

a_n=\dfrac{105}{2}

Step-by-step explanation:

Given series is

\dfrac{1}{2},\ 1,\ \dfrac{3}{2},\ 2,\ \dfrac{5}{2}.....

As we can see,

\textrm{First term},a_1=\dfrac{1}{2}

Also,

1-\dfrac{1}{2}=\dfrac{3}{2}-1=2-\dfrac{3}{3}=.....=\dfrac{1}{2}

hence, we can say given series is in arithmetic progression,

with common difference,

d=\ \dfrac{1}{2}

As given in question the nth term in A.P is given by

a_n=a_1+(n-1)d

since we have to find the 105th term, so we can write

   a_{105}=\dfrac{1}{2}+(105-1)\dfrac{1}{2}

              =\dfrac{1}{2}+\dfrac{104}{2}

              =\dfrac{105}{2}

Hence, the 105th term of given series of A.P is \dfrac{105}{2}.

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Ratling [72]

<em>**Disclaimer** Hi there! I assumed the question to be asking for a line expression. The following answer will be according to this understanding. Please let me know if I am incorrect and I will modify my answer correspondingly</em>

Answer: \Large\boxed{y-5=-\dfrac{3}{2} (x+4)}

Step-by-step explanation:

<u>Given information</u>

\text{Pass~through~point}=(x_1,~y_1)=(-4,~5)

\text{Parallel~to}:y=-\dfrac{3}{2} x-5

<u>Given equation form</u>

<em>Point-slope form is the most efficient way to write the expression</em>

\text{Point-slope form}:y-y_1=m(x-x_1)

(x_1,~y_1)=\text{A point that the line passes through}

m=\text{Slope}

<u />

<u>Determine the slope</u>

\text{Since the line is parallel to } y=-\dfrac{3}{2} x-5 \text{ , by the property of parallel}\\\text{lines, the slope of the given line is also }-\dfrac{3}{2}

\text{Therefore, m}=-\dfrac{3}{2}

<u>Substitute values into the given form</u>

y-y_1=m(x-x_1)

y-(5)=-\dfrac{3}{2} (x-(-4)

<u>Simplify the expression</u>

\Large\boxed{y-5=-\dfrac{3}{2} (x+4)}

Hope this helps!! :)

Please let me know if you have any questions

5 0
1 year ago
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Zanzabum

Answer:

Infinitely many solutions.

Step-by-step explanation:

2x+y=3

6x=9-3y

-------------

y=3-2x

6x=9-3(3-2x)

6x=9-9+6x

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Answer:

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Answer:

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Step-by-step explanation:

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