Can you get the answer and explain how you did it, i am really struggling right now

Mathematics

1 answer:

Nastasia [14]2 years ago

4 0

9514 1404 393

Answer:

453.32

Step-by-step explanation:

The argument of the summation symbol is recognizable as the general term of a geometric series with first term a1=4 and common ratio r=1.5. The indices on the summation symbol tell you that you want the sum of the first 10 terms of the series.

The general form of the sum of the first n terms of a geometric series is ...

Sn = a1(r^n -1)/(r -1)

For the given values of a1 and r, this sum is ...

$S_{10}=4\cdot\dfrac{1.5^{10}-1}{1.5-1}=4\cdot\dfrac{57.6650390625-1}{0.5}\\\\\boxed{S_{10}\approx453.32}$

____

Your graphing calculator may be able to evaluate this for you directly.

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What is the solution set of |–x| = –10?

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|a| = b gives
a =b or a = -b

so,
|-x| = -10
gives
-x = -10 or -x = 10
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now let us verify,
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so, x= 10 is NOT a solution.

when x = -10, |-(-10)| = |10| = 10 and it is not = -10
so, x= -10 is NOT a solution.

hence, this equation does not have a solution.

If we know that |...| can never be negative, we can directly deduce that this equation does not have any solution.

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