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Salsk061 [2.6K]
2 years ago
14

What is the explict formula for this sequence 5, 10, 20, 40, 80, 160, ...

Mathematics
2 answers:
serg [7]2 years ago
4 0

Answer:

a_{n} = 5(2)^{n-1}

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

10 ÷ 5 = 20 ÷ 10 = 40 ÷ 20 = 80 ÷ 40 = 2

this indicates the sequence is geometric with explicit formula

a_{n} = a₁(r)^{n-1}

where a₁ is the first term and r the common ratio

here a₁ = 5 and r = 2 , then

a_{n} = 5 (2)^{n-1}

Tcecarenko [31]2 years ago
3 0

Step-by-step explanation:

as we see in the sequence, each term is twice of the previous term.

we mark the Nth as a(N), then:

a(N)=2a(N-1)

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To solve for the value of x, it is easiest by isolating "x" to one side of the equation. This method is shown below:

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Answer:

Area of trapezium = 4.4132 R²

Step-by-step explanation:

Given, MNPK is a trapezoid

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OT = R.

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Now, sum of interior angles in a quadrilateral of 4 sides = 360°.

⇒ x + x + 65° + 65° = 360°

⇒ x = 115°.

Here, NS is a tangent to the circle and ∠NSO = 90°

consider triangle NOS;

line joining O and N bisects the angle ∠MNP

⇒ ∠ONS = \frac{115}{2} = 57.5°

Now, tan(57.5°) = \frac{OS}{SN}

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⇒ QM = \frac{2R}{2.1445}

QM = 0.9326 R .

⇒ MT = MQ + QT

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⇒ A = (\frac{NP + MK}{2}) × (ST)

       = (\frac{1.274 R + 3.1392 R}{2}) × 2 R

       = 4.4132 R²

⇒ Area of trapezium = 4.4132 R²

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4 years ago
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