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2 years ago

Helppp please quick enough points

Mathematics

1 answer:

nevsk [136]2 years ago

5 0

<h3>Geometric Sequence: a(r)ⁿ⁻¹</h3>

1) a₁ = 2, r = 3

a) First five terms: 2, 6, 18, 54, 162

b) nth term: 2(3)ⁿ⁻¹

c) The 10th term: 2(3)¹⁰⁻¹ = 39366

2) a₁ = 243, r = 1/3

a) First five terms: 243, 81, 27, 9, 3

b) nth term: 243(1/3)ⁿ⁻¹

c) The 10th term: 1/81

3) a₁ = 6, r = 2

a) First five terms: 6, 12, 24, 48, 96

b) nth term: 6(2)ⁿ⁻¹

c) The 10th term: 3072

4) a₁ = 5, r = -1/10

a) First five terms: 5, -1/2, 1/20, -1/200, 1/2000

b) nth term: 5(-1/10)ⁿ⁻¹

c) The 10th term: -5 × 10⁻⁹

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kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

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$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
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Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

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Svetradugi [14.3K]

Answer:

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Step-by-step explanation:

+6 is six more than.

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For example, let's say x=3. you gotta multiply first so you can get the five times out of the way. 3×5=15. Now we got to add six because "6 more than" means to add six. so, 15+6=21. I plugged in 21 for y to check and I got x=3, so this works.

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