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3 years ago

Complete the recursive formula of the geometric sequence -0.3, 0.9, -2.7, 8.1. ....

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

5 0

Answer:

(-1)ⁿ(3)ⁿ/10

Step-by-step explanation:

The first term a = 0.3, the second term, ar = 0.9. The common ratio r = ar/a = 0.9/-0.3 = -3.

From the general term of a geometric series,

U = arⁿ⁻¹

= (0.3)(-3)ⁿ⁻¹

= (3/10)(-3)ⁿ⁻¹

= (-1)ⁿ⁻¹(3)(3)ⁿ⁻¹/10

= (-1)ⁿ(3)ⁿ/10

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Read 2 more answers

Suppose that X has an exponential distribution with mean equal to 10. Determine the following: a. P(X > 10) b. P(X > 20) c

GrogVix [38]

Answer:

(a) The value of P (X > 10) is 0.3679.

(b) The value of P (X > 20) is 0.1353.

(d) The value of x is 30.

Step-by-step explanation:

The probability density function of an exponential distribution is:

$f(x)=\lambda e^{-\lambda x};\ x>0, \lambda>0$

The value of E (X) is 10.

The parameter λ is:

$\lambda=\frac{1}{E(X)}=\frac{1}{10}=0.10$

(a)

Compute the value of P (X > 10) as follows:

$P(X>10)=\int\limits^{\infty}_{10} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{10} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{10}\\=|e^{-0.10 x} |^{\infty}_{10}\\=e^{-0.10\times10}\\=0.3679$

Thus, the value of P (X > 10) is 0.3679.

(b)

Compute the value of P (X > 20) as follows:

$P(X>20)=\int\limits^{\infty}_{20} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{20} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{20}\\=|e^{-0.10 x} |^{\infty}_{20}\\=e^{-0.10\times20}\\=0.1353$