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3 years ago

Find the 100th term in the arithmetic sequence

Mathematics

1 answer:

fiasKO [112]3 years ago

5 0

$a_n=a_1+(n-1)d\\\\d=a_{n+1}-a_n$

$a_1=-19;\ a_2=-14;\ a_3=-9;\ a_4=-4;\ a_5=1;\ ...\\\\d=a_2-a_1=a_3-a_2=a_4-a_3=...\\\\d=-14-(-19)=-14+19=5\\\\a_n=-19+(n-1)(5)=-19+5n-5=5n-24\\\\a_{100}=5(100)-24=500-24=476\to\boxed{c.}$

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Step-by-step explanation:

Step 1:

In the triangle, the angle is 40°, the opposite side has a length of 26 units, the adjacent side has a length of x units while the hypotenuse is not given.

To determine the value of x, we determine the value of the tan of the given triangle.

To calculate the tan of angle A we divide the opposite side's length by the the adjacent side's length.

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$\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}~~
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