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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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In a collection of nickels, dimes, andquarters the value of the collection is$12.85. If the number of nickels is 6 lessthan twic
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vesna_86 [32]

Answer:

  • C. 3,75 cm

Step-by-step explanation:

<u>Ratio of corresponding sides:</u>

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7 0
3 years ago
If Mitzi has two dogs, a puppy that weighs 25 pounds and an adult that weighs 80 pounds, how much will it cost to bathe them bot
Sidana [21]

Answer:

The correct answer is A) $105

Step-by-step explanation:

In this real-world problem,  the cost to groom both dogs is (the puppy) + (the adult dog) = x.

For the first step, y = 40, if x <= 25.

y = 50, if 25 < x < 50.

if x >= 50, then y = 0.50x + 25

So therefore, substitute the puppy + adult dog = x

25 + 80 = x

105 = x

So, the final answer is $105.

It's on Edgen.

4 0
3 years ago
To find the standard deviation of the diameter of wooden​ dowels, the manufacturer measures 19 randomly selected dowels and find
loris [4]

Answer:

Option D -  [0.12

Step-by-step explanation:

Given : The manufacturer measures 19 randomly selected dowels and finds the standard deviation of the sample to be s=0.16.

To find : The​ 95% confidence interval for the population standard deviation sigma?

Solution :

Number of sample n=19

The degree of freedom is Df=n-1=19-1=18

The standard deviation of the sample is s=0.16

Applying chi-square table to find critical value,

Upper critical value of \chi^2 is UC=\chi(\frac{0.05}{2},18) = 31.5264

Lower critical value of \chi^2 is  

LC=\chi(1-\frac{0.05}{2},18) = 8.2307

Lower limit of the 95% confidence interval for the population variance

L=\frac{(df)\times (s^2)}{UC}

L=\frac{18\times (0.16^2)}{31.5264}

L=\frac{18\times0.0256}{31.5264}

L=\frac{0.4608}{31.5264}

L=0.0146

Upper limit of the 95% confidence interval for the population variance

U=\frac{(df)\times(s^2)}{LC}

U=\frac{18\times (0.16^2)}{8.2307}

U=\frac{18\times0.0256}{8.2307}

U=\frac{0.4608}{8.2307}

U=0.0559

So, The 95% confidence interval for the population variance is [0.0146, 0.0560]

Now, The 95% confidence interval for the population standard deviation is

[\sqrt{0.0146}

[0.1208

or  [0.12

Therefore, Option D is correct.

The 95% confidence interval for the population standard deviation is  [0.12

6 0
3 years ago
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