Mathematics, 05.06.2020 21:04 chrisd2432

Which of the following is a geometric sequence?

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Answer from: bokewen

The key thing to look for to determine whether a sequence is geometric is to see whether the ratio between consecutive terms - the number I would multiply one term by to get the next - is constant.

By inspection, we see that the fourth answer choice satisfies that, as $\frac{81}{27}=\frac{27}{9}=\frac{9}{3}=\frac{3}{1}=3.$ Why not the first? We have $2=\frac{12}{6}\ne\frac{6}{2}=3.$

The third choice is not a geometric sequence, but rather an arithmetic sequence, where the difference between consecutive terms is constant. Just to make sure that it isn't geometric, we compute $\frac{14}{9}\ne\frac{9}{4}.$

The second sequence is not geometric (although it does eventually converge to 1, but not its corresponding series), as $\frac{4}{3}=\frac{2/3}{1/2}\ne\frac{3/4}{2/3}=\frac{9}{8}.$

Answer from: Quest

1/5

step-by-step explanation:

the dice has 6 sides and there is only one 5 in a dice.

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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