An arithmetic sequence (a_n) is as follows:
where
is the first term and d is the constant difference,
thus, we see that the n'th term of an arithmetic sequence is
in our particular case d=5, the third term is 8, so we have:
and the general term is
,
Answer: first term is -2, n'th term is -2+5(n-1)
The value of x in the secants intersection is 1 units
The value of NM in the tangent and secant intersection is 51 units
<h3>How to find length when secant and tangent intersect?</h3>
The first question, two secant intersect outside the circle.
Therefore,
(6x + 8x)8x = (9 + 7)7
14x(8x) = 16(7)
112x² = 112
x² = 112 / 112
x = √1
x = 1
The second question, tangent and secant intersect,
Therefore,
(x + 3)² = (x - 3)(16 + x - 3)
(x + 3)² = (x - 3)(x + 13)
(x + 3)(x + 3) = (x - 3)(x + 13)
x² + 3x + 3x + 9 = x² + 13x - 3x - 39
x² + 9x + 9 = x² + 10x - 39
x² - x² + 9x - 10x = -39 - 9
-x = - 48
x = 48
NM = 48 + 3 = 51 units
learn more on secant and tangent here: brainly.com/question/12477905
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X + x + 36 = 90
2x = 54
x = 27 Answer
The given expression is ![3b^2*(\sqrt[3]{54a}) + 3*(\sqrt[3]{2ab^6})](https://tex.z-dn.net/?f=%203b%5E2%2A%28%5Csqrt%5B3%5D%7B54a%7D%29%20%2B%203%2A%28%5Csqrt%5B3%5D%7B2ab%5E6%7D%29%20)
This can be simplified as :
= ![3*b^2*(\sqrt[3]{27 *2*a}) + 3*(\sqrt[3]{2*a*b^6})](https://tex.z-dn.net/?f=%203%2Ab%5E2%2A%28%5Csqrt%5B3%5D%7B27%20%2A2%2Aa%7D%29%20%2B%203%2A%28%5Csqrt%5B3%5D%7B2%2Aa%2Ab%5E6%7D%29%20)
We know that: ![\sqrt[3]{27} = 3](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B27%7D%20%20%3D%203%20%20%20)
Similarly we also can simplify: ![\sqrt[3]{b^6} = b^2](https://tex.z-dn.net/?f=%20%20%5Csqrt%5B3%5D%7Bb%5E6%7D%20%20%3D%20b%5E2%20)
So our expression will look like this:
= ![3*3*b^2*(\sqrt[3]{2a}) + 3*b^2*(\sqrt[3]{2a})](https://tex.z-dn.net/?f=%203%2A3%2Ab%5E2%2A%28%5Csqrt%5B3%5D%7B2a%7D%29%20%2B%203%2Ab%5E2%2A%28%5Csqrt%5B3%5D%7B2a%7D%29%20)
= ![9b^2*(\sqrt[3]{2a}) + 3b^2*(\sqrt[3]{2a})](https://tex.z-dn.net/?f=%209b%5E2%2A%28%5Csqrt%5B3%5D%7B2a%7D%29%20%2B%203b%5E2%2A%28%5Csqrt%5B3%5D%7B2a%7D%29%20)
=![\sqrt[3]{2a}*(9b^2 + 3b^2)](https://tex.z-dn.net/?f=%20%20%5Csqrt%5B3%5D%7B2a%7D%2A%289b%5E2%20%2B%203b%5E2%29%20)
=![\sqrt[3]{2a}*(12b^2)](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B2a%7D%2A%2812b%5E2%29%20)
This can also be written as:
![12b^2(\sqrt[3]{2a})](https://tex.z-dn.net/?f=%2012b%5E2%28%5Csqrt%5B3%5D%7B2a%7D%29%20)
So the Answer is Option B
