The 15th and 21st terms of an arithmetic sequence are -67 and -97, what is the 30th term?

Mathematics

1 answer:

natka813 [3]3 years ago

7 0

I believe it would be -132.

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Answer:

Step-by-step explanation:

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victus00 [196]

<h2>Explanation:</h2>

Here we have the following expression:

$(csc x - 1) (csc x + 1)$

So we need to extend this. Remember that the difference of squares tells us:

$(a-b)(a+b)=a^2-b^2$

So here:

$a=cscx \\ \\ b=1$

Thus:

$(csc x - 1) (csc x + 1)=csc^2x-1 \\ \\ \\ But: \\ \\ cscx=\frac{1}{sinx} \\ \\ \\ Then: \\ \\ csc^2x-1=\frac{1}{sin^2x}-1=\frac{1-sin^2x}{sin^2x}=\frac{cos^2x}{sin^2x}=cot^2x \\ \\ \\ Finally: \\ \\ \boxed{(csc x - 1) (csc x + 1)=cot^2x}$