What is the explicit formula for this sequence? 2,10,50,250,1250

Mathematics

2 answers:

Zina [86]3 years ago

8 0

Answer:

This is a geometric sequence with a₁ = 2 and r = 5 where a₁ is the first term and r is the common ratio.

Explicit formula: aₙ = a₁ * r ⁿ⁻¹

The answer is aₙ = 2 * (5ⁿ⁻¹)

Valentin [98]3 years ago

4 0

Answer:

$a_n = 2(5)^{n-1}$

Step-by-step explanation:

Explicit Geometric Formula: $a_n = a_1r^{n-1}$

a₁ is 1st term

r is common ratio

n is term number

Step 1: Find common ratio r

r = 10/2 = 5

Step 2: Plug variables into formula

$a_n = 2(5)^{n-1}$

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What is the maximum slope to f(x)= e^(-x^2)?

MA_775_DIABLO [31]

F'(x)=-2x{e^(-x²)}
Equating f'(x)=0,
i.e,

-2x{e^(-x²)}=0....eqn(i)
For maximum slope:
Differentiating (i) wrt x,we get,
4x² {e^(-x²)}-2 {e^(-x²)}=0
{e^(-x²)} [4x²-2]=0
4x²-2=0
x=1/√2

If f(x)=y then f'(x)=dy/dx=slope
So,
Maximum slope
= f'(x)
= -2x{e^(-x²)}
=-2×(1/✓2){e^(-1/✓2)²}
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6 0

2 years ago

3x^2+16x^2+x+7-10x^2+22+15x-6x

lord [1]

Answer:

9x^2 + 10x + 29

Step-by-step explanation:

Let's sort the x^2, the x and the numbers without an x:

First, the x^2

3x^2 + 16x^2 - 10x^2

So that's 3 + 16 - 10 if we ignore the x^2.

We can simplify this to 9x^2, because 3+16-10=9.