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Alexandra [31]
3 years ago
5

What is the 5th term of the geometric sequence a1=120, a2=36, a3=10.8, a6=0.2916

Mathematics
2 answers:
Serggg [28]3 years ago
6 0
The fifth term of the geometric sequence would be 0.972
Dmitry_Shevchenko [17]3 years ago
3 0

A geometric sequence is given by terms a₁ = 120, a₂ = 36, a₃ = 10.8, a₆ = 0.2916.

The First term is given, a = 120.

Common ratio (r) would be ratio of second term to first term i.e.

r=\frac{a_{2}}{a_{1}} = \frac{36}{120} = 0.3

The formula for n-th term of geometric sequence is given by as follows :-

a_{n} =a*r^{n-1}

It says to find 5th term of this given geometric sequence. For 5th term, n = 5.

a_{5} =120*(0.3)^{5-1} \\\\ a_{5} =120*(0.3)^{4} \\\\ a_{5} =120*(0.0081) \\\\ a_{5} =0.972

Hence, a₅ = 0.972 would be 5th term of the given geometric sequence.

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A local gym had 490 members last quarter. This quarter, with a change in its rates, it has 686 members. What is the percent of i
sergij07 [2.7K]

Given:

Number of gym members in last quarter = 490

Number of gym members in this quarter = 686

To find:

The percent of increase in the number of members.

Solution:

We have,

Number of gym members in last quarter = 490

Number of gym members in this quarter = 686

Now, the percent of increase in the number of members.

\%\text{ of increase}=\dfrac{{Members in this month - Members in last month}}{\text{Members in last month}}\times 100

\%\text{ of increase}=\dfrac{686-490}{490}\times 100

\%\text{ of increase}=\dfrac{196}{490}\times 100

\%\text{ of increase}=\dfrac{2}{5}\times 100

\%\text{ of increase}=2\times 20

\%\text{ of increase}=40

Therefore, the gym members increased by 40%.

4 0
3 years ago
X2 – 7x + 6 = -8<br> solve using factoring
murzikaleks [220]

Answer:

Step-by-step explanation:

Rewrite this in standard quadratic equation form:  x^2 - 7x +  6 + 8 = 0, or x^2 - 7x + 14 = 0.  This does not factor easily, so I will use the quadratic formula to find the roots and then write out the factors based upon the roots:

The discriminant is b^2 - 4ac, which here is (-7)^2 - 4(1)(14) = -7.

Because the discriminant is negative, we know that there are two unequal, complex roots.  They are:

      -(-7) ± i√7         7 ± i√7

x = ----------------- = ---------------

              2                     2

One factor is (x - [1/2]{7 ± √7}  )

7 0
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lesya [120]
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In the triangle below, what is csc θ?
earnstyle [38]
It si cool so basicly u take 5 divide bye 13 times 5

8 0
3 years ago
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boyakko [2]

Answer:

81 7/12

Step-by-step explanation:

75 5/12 - (-6 1/6)= 81 7/12

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