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Butoxors [25]
3 years ago
8

What is the sum of the arithmetic sequence 3, 9, 15..., if there are 26 terms?

Mathematics
2 answers:
masya89 [10]3 years ago
7 0

<span><span>9 - 3 = 6, 15-9 = 6 the difference is 6, So d = 6
</span><span>
First term: a1 = 3


Sn = n*(a1 + an)/2

Sn = n*(a1 + a1 + (n-1)*d)/2

Sn = n*(2*a1 + (n-1)*d)/2

</span></span>

<span> <span>substitute 26 for n
</span> S26 = 26*(2*a1 + (26-1)*d)/2 </span>

<span><span>substitute 3 for a1
</span><span>
S26 = 26*(2*3 + (26-1)*d)/2 </span></span>

<span><span>substitute 6 for d
</span><span>
S26 = 26*(2*3 + (26-1)*6)/2 </span><span> 
</span><span>
S26 = 2,028</span></span><span><span>
</span><span>
</span></span>


marissa [1.9K]3 years ago
3 0
Sum of an arithmetic series is:

S = n*(a_1+a_n)/2, that easy.

n is the number of terms, 26 in your case. a_n is a_26. We need to find the series!

a_n = a_1 + (n-1)*d, the difference, d, is 6.

So a_n = 3 + (n-1)*6 = 6*n-3 (check it works: 3, 9, 15, ...)

Now a_26 = 6*26-3 = 153, so finally:

S = 26*(3+153)/2 = 26*78 = 2028

2028 is the answer

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D

Step-by-step explanation:

For some side lengths to create a triangle, any two of the side lengths must have an added length together of less than the third leg. Otherwise, the vertices would simply not be able to be connected by the lines. In a), 3+5=8, but since it is not more, the triangle will not be able to be formed (it would basically just be a line.) In B, 7+8< 16. In C, there is the same situation as with the first example (4+15=19). Finally, in the last one, 5+7>12, and all of the side lengths work out. Therefore, the correct answer is D. Hope this helps!

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3 years ago
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Answer:

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Step-by-step explanation:

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Which would also equal to 6 x 5^2.

If you do this, you will find that the answer is 150 units^2.

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3 years ago
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3 years ago
Add or subtract. Write the answer is simplest form.
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3 years ago
William works at a nearby electronics store. He makes a commission of 6% percent on everything he sells. If he sells a computer
Naddika [18.5K]

Commission earned by William is $ 45.84

<h3><u>Solution:</u></h3>

Given that,

William makes a commission of 6% percent on everything he sells

He sells a computer for $764.00

<em><u>To find: Commission amount of William</u></em>

Given that he makes a commission of 6 % on everything he sells. So he has received a commission of 6 % of $ 764.00

Commission amount of William = 6 % of $ 764.00

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8 0
3 years ago
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