What is the explicit rule for this geometric sequence? 2, 6, 18, 54, …

Mathematics

1 answer:

Alex787 [66]2 years ago

6 0

Answer:

A term at position n can be expressed as \[2*3^{n-1}\]

Step-by-step explanation:

The given geometric sequence is 2, 6, 18, 54, …

Starting term = 2

Second term = 6

So second term is 3 times the first term.

Similarly, Third term = 18

This is 3 times the second term, that is , 3 * 6

Fourth term is is 54.

This is 3 times the third term, that is , 3 * 18

Generalizing, a term in the sequence can be expressed as \[2*3^{n-1}\]

where n represents the position of the term in the sequence.

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Solve for x. The triangles in each pair are similar. <br>

KatRina [158]

Answer:

Step-by-step explanation:

You need to pay very close attention to the triangle similarity statement. This says that triangle NML is similar to triangle NVU. But if you look at the way that triangle NVU is oriented in its appearance, it's laying on its side. We need to set it upright so that angle N is the vertex angle, angle V is the base angle on the left, and angle U is the base angle on the right. When we do that we see that sides NV and NM are corresponding and exist in a ratio to one another; likewise with sides VU and ML. Setting up the proportion:

$\frac{NV}{NM}=\frac{VU}{ML}$