Find the values of the unknown constants for the identities

Mathematics

1 answer:

ankoles [38]4 years ago

5 0

Answer:

a = 1 and b = - 10

Step-by-step explanation:

Expand the right side of the identity

x(ax² - 3x + b) - 3(ax² - 3x + b)

= ax³ - 3x² + bx - 3ax² + 9x - 3b

= ax³ - x²(3 + 3a) + x(b + 9) - 3b

Equate the coefficients of like terms on both sides of the identity

x³ terms → ax³ with x³ ⇒ a = 1

x terms → - x with (b + 9)x ⇒ b + 9 = - 1 ⇒ b = - 10

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A recursive arithmetic sequence is defined ad f(1)=6, f(n+1)=f(n)+5 for n>1. The first four terms of the sequence are shown i

Dennis_Churaev [7]

Write the first few terms of the sequence.
f₁ = 6
f₂ = f₁ + 5 = 11
f₃ = f₂ + 5 = 16
f₄ = f₃ + 5 = 21
and so on

The sequence is
6, 11, 16, 21, ...,
This is an arithmetic sequence with a common difference of 5.

In function notation, the sequence is
$f_{n+1} = 6 + 5n, \\ \, n=0,1,2, \, ...,$

This represents the equation of a straight line with n as the independent variable and f as the dependent variable.
The slope is 5.
A graph of the line is shown below.

Answer:
The sequence is $f_{n+1} = 6 + 5n, \,\, n=0,1,2, \, ...,$
The slope is 5.