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2 years ago

A straight line passes through the points P (1, 2) and Q (5, - 14). What is the gradient of the the line PQ?

Mathematics

1 answer:

ddd [48]2 years ago

5 0

Answer:

Step-by-step explanation:

gradient= change in y

__________

change in x

m= y2_ y1

______

x2- x1

m= -14- 2

_____

5-1

m= -16

___

m= -4

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Write an explicit formula for the An, and the n^th term of the sequence 24,-12,6,....

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Answer:

$T_n = -48* (-\frac{1}{2})^{n}$

Step-by-step explanation:

Given

$24, -12, 6,...$

Required

Write a formula

The above sequence shows a geometric sequence because:

$r = \frac{-12}{24} = \frac{6}{-12} = -\frac{1}{2}$ -- common ratio

The equation is determined using:

$T_n = ar^{n-1}$

Where

$a = 24$

Substitute values for a and r

$T_n = 24* (-\frac{1}{2})^{n-1}$

Apply law of indices:

$T_n = 24* (-\frac{1}{2})^{n} * (-\frac{1}{2})^{-1}$

$T_n = 24* (-\frac{1}{2})^{n} * 1/(-\frac{1}{2})$

$T_n = 24* (-\frac{1}{2})^{n} * 1*-2$

$T_n = 1*-2*24* (-\frac{1}{2})^{n}$

$T_n = -48* (-\frac{1}{2})^{n}$

The above represents the explicit formula

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3 years ago

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Answer:

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Step-by-step explanation:

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