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DIA [1.3K]
3 years ago
5

What is the value of the fourth term in a geometric sequence for which a1= 30 and r = 1/2

Mathematics
1 answer:
Viktor [21]3 years ago
4 0

Answer:

a_{4} = 3.75

Step-by-step explanation:

The n th term of a geometric sequence is

a_{n} = a₁(r)^{n-1}

where a₁ is the first term and r the common ratio

Here a₁ = 30 and r = \frac{1}{2}, thus

a_{4} = 30(\frac{1}{2}) ^{3} = 30 × \frac{1}{8} = \frac{30}{8} = \frac{15}{4} = 3.75

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Hi!
This is a fun one, as it delves into basic trigonometry.

We're going to use the Pythagorean theorem here, which says that for right triangles where "c" is the hypotenuse,

a² + b² = c²

We have to split this large triangle into two parts, both of which are right triangles. (This is why they drew a line in the middle to tell you that the larger triangle is composed of two right triangles.)

Let's do the one on the right first.

We know that the length of the hypotenuse is 10, and that the length of one of the legs is 6.5. If we plug this into our equation, we'll get the length of the other leg. I'm choosing "b" to be 6.5, but it really doesn't matter if you pick "a" or "b", so long as you reserve "c" for the hypotenuse (longest side).

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Have a great one!
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