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Rashid [163]
3 years ago
15

What is the 214 term in the sequence 7,10,13,16?

Mathematics
1 answer:
mixer [17]3 years ago
5 0
We can figure this out using the explicit formula.

f(n)=f(1)+d(n-1)

n represents the term we are looking for.
f(1) represents the first term in the sequence, which in this case, is 7.
d represents the common difference, which in this case, is +3.

f(n) = 7 + 3(n - 1)
f(n) = 7 + 3n - 3
f(n) = 4 + 3n

Now, we can input 214 for n and solve.

f(214) = 4 + 3(214)
f(214) = 4 + 642
f(214) = 646

The 214th term in this sequence is 646.
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Answer:

1. The ratio of their diameters is 8/5 = 8 : 5

2. The ratio of their surface area is (8/5)²

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Step-by-step explanation:

Given that the two cylinders are similar, we have;

Two cylinders are similar when the ratio of their heights is equal to the ratio of their radii

Therefore, we have;

1. The ratio of the height of the two cylinders = 8/5 = The radio of their radii = r₁/r₂

The ratio of their diameter = D₁/D₂ = 2·r₁/2·r₂ = r₁/r₂ = 8/5

The ratio of their diameters D₁/D₂ = 8/5 = 8 : 5

2. The surface area of the cylinders = 2·π·r·h + 2·π·r²

Therefore, we have;

(2·π·r₁·h₁ + 2·π·r₁²)/(2·π·r₂·h₂ + 2·π·r₂²) = (r₁·h₁ + r₁²)/(r₂·h₂ + r₂²)

h₁ = h₂ × 8/5

r₁ = r₂ × 8/5

= (8/5)²(r₂·h₂ + r₂²)/(r₂·h₂ + r₂²)  = (8/5)²

The ratio of their surface area = (8/5)²

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The ratio of their volume = (8/5)³

4. The ratio of the area of the base of the larger cylinder to the area of the base of the smaller cylinder is (8/5)²

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Answer:

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