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EastWind [94]
3 years ago
13

Find an equation for the nth term of the arithmetic sequence. a15 = -53, a16 = -5

Mathematics
2 answers:
lesantik [10]3 years ago
5 0
48n-773 is the equation for the nth term
ddd [48]3 years ago
3 0

Answer:  The required equation for the n-th term is a_n=-773+48n.

Step-by-step explanation:  We are given to find the equation for the nth term of the arithmetic sequence with the fifteenth and sixteenth term as follows :

a_{15}=-53,~~~a_{16}=-5.

We know that

the nth term of an arithmetic sequence with first term a and common difference d is given by

a_n=a+(n-1)d.

So, we have

a_{15}=-53\\\\\Rightarrow a+(15-1)d=-53\\\\\Rightarrow a+14d=-53~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

and

a_{16}=-5\\\\\Rightarrow a+(16-1)d=-5\\\\\Rightarrow a+15d=-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

Subtracting equation (i) from equation (ii), we get

(a+15d)+(a+14d)=-5-(-53)\\\\\Rightarrow d=48.

And, from equation (i), we get

a+14\times48=-53\\\\\Rightarrow a+672-53\\\\\Rightarrow a=-725.

Therefore, the n-th term of the given sequence is

a_n=a+(n-1)d\\\\\Rightarrow a_n=-725+(n-1)48\\\\\Rightarrow a_n=-773+48n.

Thus, the required equation for the n-th term is a_n=-773+48n.

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Andre45 [30]
I would try going with h =7/2 if that is wrong just rate me 1
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3 years ago
What is the greatest common factor of 73 and 30
sergij07 [2.7K]

Answer:1

Step-by-step explanation:

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4 0
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Read 2 more answers
A phone company offers two monthly plans. Plan A costs $10 plus an additional $0.15 for each minute of calls. Plan B costs $30 p
Mkey [24]

First, you need to write to expressions to model each situation:

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Next, set the expressions equal to each other and solve for x:

10+0.15x=30+0.1x

<em>*Subtract 0.1x from both sides to isolate the variable*</em>

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<em>*Subtract 10 from both sides*</em>

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The plans would have the same cost after 400 minutes of calls.


To find how much money the plans cost at 400 minutes, plug 400 into either expression.  We'll use Plan A:

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Hope this helps!

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3 years ago
0=x^2- 10x+10<br> Rewrite the equation by completing the square
zubka84 [21]

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4 0
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xeze [42]

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Hope I helped! ☺☼

8 0
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