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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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Ieda and Thanh both offer piano lessons. Ieda charges an initial fee of $8.50 and an hourly rate of $11.00. Thanh charges an ini
Verizon [17]

Answer:

after 3 hours of instruction.

Step-by-step explanation:

First, start by setting up the equation.

Leda charges an initial fee, meaning this fee is only going to be one time. However, there is an hourly rate of 11. Since we do not know how many hours these piano lessons are going to last, we put a variable (I will use x), after this number.

The initial fee is 8.50. There needs to be a variable after 11 because that is the number we don't know.

The equation for Leda's lessons are <em>8.50+11.00x. </em>

Now, we need to find out what the equation for Thanh's lessons are going to be, because we're going to be setting both equations equal to each other to find out when they cost the same. At the moment both equal each other, is when they are the same amount.

Thanh's equation also has an intial fee and an hourly rate. So, the equation will be

<em>10.00+10.50x. </em>

Now we solve.

<em>8.50+11.00x = 10.00+10.50x </em>

First, subtract from both sides. We will do the numbers without variables first.

<em>8.50+11.00x = 10.00+10.50x </em>

<em>-8.50               -8.50 </em>

<em>____________________</em>

<em>0     +11.00x =   1.50 +10.50x</em>

Then, subtract the x's. (taking away the zero because it is equivalent to nothing)

<em>11.00x =   1.50 +10.50x</em>

<em>- 10.50x            -10.50x</em>

<em>__________________</em>

<em>0.50x = 1.50 </em>

Lastly, to find out the answer, we divide.

1.50/0.50= 3.

<u>To check your answer, you can plug into the original equation. </u>

<em>8.50+11.00 times 3 = 10.00+10.50 times 3 </em>

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ivanzaharov [21]

Answer:

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Step-by-step explanation:

Information given

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gizmo_the_mogwai [7]

Question:

The local community theater sold a total of 240 tickets for Saturday night’s performance. They sold 180 more full-price tickets than discount tickets. Which system of equations can be used to model this situation?

Answer:

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Step-by-step explanation:

Given

Tickets = 240

Represent the number of full price with x and discounted price with y.

From the question:

x = 180 more than y

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x = 180 + y

Also, a total of 240 were sold.

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x + y = 240

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Solving further;

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<em />

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