Which recursive definition produces an arithmetic sequence where g(5) = 8 and g(10) = 10?

gₙ = gₙ₋₁ + 0.4, with g₁ = 6.4

Step-by-step explanation:

The n-th term of an arithmetic sequence can be written as:

gₙ = g₁ + (n - 1)*d

Where g₁ is the first value, and d is the difference between any two consecutive terms of this sequence.

Then we have the equations:

g₅ = 8 = g₁ + (5 -1)*d

g₁₀ = 10 = g₁ + (10 - 1)*d

This is a system of equations, we can rewrite this as:

8 = g₁ + 4*d

10 = g₁ + 9*d

To solve this, the first step will be isolate one of the variables in one of the equations, i will isolate g₁ in the first equation:

g₁ = 8 - 4*d

Now we can replace this in the second equation to get:

10 = 8 - 4*d + 9*d

10 = 8 + 5*d

10 - 8 = 5*d

2 = 5*d

2/5 = d = 0.4

Now with this, we can find the value of g₁ by using the equation:

g1 = 8 - 4*d = 8 - 4*(2/5) = 8 - 8/5 = 6.4

Then the nth term of this sequence can be written as:

gₙ = 6.4 + (n - 1)*0.4

This relation also can be written as:

gₙ = gₙ₋₁ + d = gₙ₋₁ + 0.4, with g₁ = 6.4

Then the correct option is the second option.

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!

it could be 1,3 and more others to create a cylinder.

step-by-step explanation: