Answer:
The most correct option for the recursive expression of the geometric sequence is;
4. t₁ = 7 and tₙ = 2·tₙ₋₁, for n > 2
Step-by-step explanation:
The general form for the nth term of a geometric sequence, aₙ is given as follows;
aₙ = a₁·r⁽ⁿ⁻¹⁾
Where;
a₁ = The first term
r = The common ratio
n = The number of terms
The given geometric sequence is 7, 14, 28, 56, 112
The common ratio, r = 14/7 = 25/14 = 56/58 = 112/56 = 2
r = 2
Let, 't₁', represent the first term of the geometric sequence
Therefore, the nth term of the geometric sequence is presented as follows;
tₙ = t₁·r⁽ⁿ⁻¹⁾ = t₁·2⁽ⁿ⁻¹⁾
tₙ = t₁·2⁽ⁿ⁻¹⁾ = 2·t₁2⁽ⁿ⁻²⁾ = 2·tₙ₋₁
∴ tₙ = 2·tₙ₋₁, for n ≥ 2
Therefore, we have;
t₁ = 7 and tₙ = 2·tₙ₋₁, for n ≥ 2.
Answer:
2s+5p=40
Step-by-step explanation:
s=sodas
p=popcorn
you can plug in 0 for s or for p to see how many of the other she can get (if you plug in 0 for s you see she can get 8 popcorns, if you plug in 0 for popcorn, she can buy 20 sodas)
Answer:
f(x) = - 9x² + 9
g(x) = 8x² + 9x
To find (f+g)(x) add g(x) to f(x)
That's
(f+g)(x) = -9x² + 9 + 8x² + 9x
Group like terms
(f+g)(x) = - 9x² + 8x² + 9x + 9
<h3>(f+g)(x) = - x² + 9x + 9</h3>
To find (f + g)(- 1) substitute - 1 into (f+g)(x)
That's
(f + g)(- 1) = -(-1)² + 9(-1) + 9
= - 1 - 9 + 9
<h3>= - 1</h3>
Hope this helps you
Answer:
kindly check the solution in figure below.
Step-by-step explanation:
Answer:
second option
Step-by-step explanation:
Given x = a, x = b are roots of f(x) then the factors are
(x - a) and (x - b)
and f(x) is the product of the factors
f(x) = a(x - a)(x - b) ← where a is a multiplier
If the roots have multiplicity then the factor is repeated
x = a with multiplicity 2, then factors are (x - a) and (x - a)
Here a = 2
x = - 4 with multiplicity 3, thus factors (x + 4 ), (x + 4), (x + 4)
x = 10 with multiplicity 1 has factor (x - 10)
Thus the polynomial function is
f(x) = 2(x + 4)(x + 4)(x + 4)(x - 10)
