9514 1404 393
Answer:
5) 729, an=3^n, a[1]=3; a[n]=3·a[n-1]
6) 1792, an=7(4^(n-1)), a[1]=7; a[n]=4·a[n-1]
Step-by-step explanation:
The next term of a geometric sequence is the last term multiplied by the common ratio. (This is the basis of the recursive formula.)
The Explicit Rule is ...
for first term a₁ and common ratio r.
The Recursive Rule is ...
a[1] = a₁
a[n] = r·a[n-1]
__
5. First term is a₁ = 3; common ratio is r = 9/3 = 3.
Next term: 243×3 = 729
Explicit rule: an = 3·3^(n-1) = 3^n
Recursive rule: a[1] = 3; a[n] = 3·a[n-1]
__
6. First term is a₁ = 7; common ratio is r = 28/7 = 4.
Next term: 448×4 = 1792
Explicit rule: an = 7·4^(n-1)
Recursive rule: a[1] = 7; a[n] = 4·a[n-1]
Let the smaller number be x.
Given, the larger number is 7 times the smaller number.
So, the larger number = 7x.
Given, 3 times the larger number is 7 more than 4 times the smaller number.
So we can write the equation as,
Now we have to move 4x to the left side by subtracting 4x from both sides.
To get x, we will divide both sides by 17. We will get,
So the smaller number =
The larger number = =
So we have got the required numbers.
Smaller number = and larger number = .
The slope is -1/4 and the y intercept it -6
The point halfway between two end points is called a midpoint