Find the indicated term of the given geometric sequence, a1=18, r=2.1, n=12

1 answer:

6 0

The general term of a geometric sequence is
an = a1·r^(n-1)
Fill in the given numbers and do the arithmetic.
a12 = 18·2.1^(12-1)
a12 = 63,049.95009759978

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When a number with one decimal place is raised to the 11th power, the result is a number with 11 decimal places. It would seem you are expected to round this to some lesser number of decimal places. The number shown is exact. You can round it according to your needs.

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Line AC is tangent to circle O at point C What is the measure of OAC?

Nuetrik [128]

AC is a tangent so by definition, it touches the circle at exactly one point (point C) and forms a right angle at the tangency point. So angle ACO is 90 degrees

The remaining angle OAC must be 45 degrees because we need to have all three angles add to 180
45+45+90 = 90+90 = 180

Alternatively you can solve algebraically like so
(angle OAC) + (angle OCA) + (angle COA) = 180
(angle OAC) + (90 degrees) + (45 degrees) = 180
(angle OAC) + 90+45 = 180
(angle OAC) + 135 = 180
(angle OAC) + 135 - 135 = 180 - 135
angle OAC = 45 degrees

Side Note: Triangle OCA is an isosceles right triangle. It is of the template 45-45-90.

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