Finding the general formula of A1 = 2, A2 = 6, A3 = 14, A4 = 30

Finding the general formula of A1 = 2, A2 = 6, A3 = 14, A4 = 30

a2-a1=6-2=2^2
a3-a2=14-6=2^3
a4-a3=30-14=2^4
.
an-a(n-1)=2^n
Add the above expressions to get:
an-a1=2^2+2^3+2^4+...+2^n
=4*[1-2^(n-1)]/(1-2)
=4*[2^(n-1)-1]
=2^(n+1)-4
an=2^(n+1)-2

1 / 2 (a-b) + 3 (2a-b) - (3a-b), where a = 2, B = - 1

1 / 2 (a-b) + 3 (2a-b) - (3a-b)
=1/2a-1/2b+6a-3b-3a+b
=5/2a-5/2b
=5/2x2+5/2x1
=5+2.5
=7.5

Find the following problem: (3a ^ 2-15a + 21) / (a ^ 2-5A + 6) - (2a ^ 2-6a + 1) / (a ^ 2-3a + 2)

(3a²-15a+21)/(a²-5a+6)-(2a²-6a+1)/(a²-3a+2)=3+3/(a²-5a+6)-2+3/(a²-3a+2)=1+3/(a-3)-3/(a-2)+3/(a-2)-3/(a-1)=1+3/(a-3)-3/(a-1)

(3a^2-15a+21)/(a^2-5a+6)-(2a^2-6a+1)/(a^2-3a+2)

(3a^2-15a+21)/(a^2-5a+6)-(2a^2-6a+1)/(a^2-3a+2)
=(3a^2-15a+21)/(a-2)(a-3)-(2a^2-6a+1)/(a-2)(a-1)
=[(3a^2-15a+21)(a-1)-(2a^2-6a+1)(a-3)]/(a-1)(a-2)(a-3)
=[(3a^3-18a^2+36a-21)-(2a^3-12a^2+19a-3)]/(a-1)(a-2)(a-3)
=(a^3-6a^2+17a-18)/(a-1)(a-2)(a-3)
=(a-2)(a^2-4a+9)/(a-1)(a-2)(a-3)
=(a^2-4a+9)/(a-1)(a-3)

A is any rational number. The following formulas are correct: 1.3A ＞ 4A 2. A / 3 ＜ A / 43. A ＞ - A4, 1-A ＞ 1 / 2-a

A is any rational number. The following formulas are correct: 1.3A ＞ 4A 2. A / 3 ＜ A / 43. A ＞ - A4, 1-A ＞ 1 / 2-a
The title is incomplete

[cube of 3 (a + b) - square of 2 (a + b) - 4a-4b]

3(a+b)³-2(a+b)²-4a-4b=（a+b)【3(a+b)²-2(a+b)-4】=(a+b)(a+b-2)【3(a+b)+2】

[cube of 3 (a + b) - square of 2 (a + b) - 4a-4b] / (a + b)

Original formula = [3 (a + b) & #179; - 2 (a + b) & #178; - 4 (a + b)] / (a + b)
=3(a+b)³÷(a+b)-2(a+b)²÷(a+b)-4(a+b)÷(a+b)
=3(a+b)²-2(a+b)-4

The third power of a-the square of a-4a + 7 = 3

a*3-a*2-4a+7=3
a*3-a*2-4a+4=0
a(a*2-4)-(a*2-4)=0
(a*2-4)(a-1)=0
A = 2 and a = 1

0.4a+0.4*70%*(84-a)=30.72

0.4a+28%(84-a)=30.72
40a+28(84-a)=3072
12a=720
a=60

0.4A + 70% x0.4 (84-A) = 30.72 complete process

0.4a+70%x0.4(84-a)=30.72
Multiply both sides of the equation by 100
40a+70*0.4(84-a)=3072
Divide both sides of the equation by 4
10a+8(84-a)=768
10a+672-8a=768
2a=768-672
2a=96
a=48