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Anastaziya [24]
3 years ago
5

Consider the sequence 3, 6, 12, 24, 48, .... (a) Write a recursive rule to represent the sequence. (b) Write an explicit rule to

represent the sequence. (c) Find the 15th term in the sequence.
Mathematics
1 answer:
saveliy_v [14]3 years ago
5 0

Answer:

  a. a[1] = 3; a[n] = 2a[n-1]

  b. a[n] = 3·2^(n-1)

  c. a[15] = 49,152

Step-by-step explanation:

Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.

The first term is 3, and the common ratio is 2.

<h3>(a)</h3>

The recursive rule is ...

  a[1] = 3

  a[n] = 2×a[n-1]

__

<h3>(b)</h3>

The explicit rule is ...

  a[n] = a[1]×r^(n-1)

  a[n] = 3×2^(n-1)

__

<h3>(c)</h3>

The 15th term is ...

  a[15] = 3×2^(15-1) = 3×2^14

  a[15] = 49,152

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3 0
3 years ago
Interpret the following sine regression model.
natita [175]

Answer:

The question is incomplete, so I will describe the sine regression model.

The function

y = 0.884 sin(0.245x - 1.093) + 0.400

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y = a sin(bx - c) + d

where:

a = 0.884

b = 0.245

c = 1.093

d = 0.400

The amplitude of the function is computed as follows:

amplitude = |a| = 0.884

The period of the function is computed as follows:

period = 2π/|b| = 25.6456

The phase shift of the function is computed as follows:

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3 0
4 years ago
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Natali5045456 [20]
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6 0
3 years ago
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A farmer Has 900 yards of fencing to enclose a rectangular pasture for her goats. Since one side of the pasture borders a river,
horsena [70]

Answer:

Length, l=450 yards

Width, b=225 yards

Step-by-step explanation:

Let the long side be x and since the length is twice the width, then the width is half of that length hence 0.5x. Since we only have three parts to fence as one long side doesn't require fencing, then the perimeter will be given by x+0.5x+0.5x=2x=900 yards

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7 0
3 years ago
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mihalych1998 [28]
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for the second one u do the same thing.
4 0
3 years ago
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