Find the first five terms of the sequence in which a1 = –10 and an = 4an – 1 + 7, if n ≥ 2.

The new sequence

-40, -160, -640, -2560, -10240, -40960

Step-by-step explanation:

It is given that,

aₙ = 4a₍ₙ₋₁₎ and a₁ = -10

To find the first 7 terms of the sequence

a₁ = -10

a₂ = 4a₁ = 4 * (-10) = -40

a₃ = 4a₂ = 4 * (-40) = -160

a₄ = 4a₃ = 4 * ( -160) = -640

a₅ = 4a₄ = 4 * (-640) = -2560

a₆ = 4a₅ = 4 * (-2560) = -10240

a₇ = 4a₆ = 4 * (-10240) = -40960

Therefore the new sequence

-40, -160, -640, -2560, -10240, -40960

Given Below

Step-by-step explanation:

Given

 for n greater than equal to 2

using above equation

The cost of 16 pencils and 10 notebooks is $5.84.

Explanation: You can solve this using linear systems:

Let X be the cost per pencil, and let Y be the cost per notebook.

(1) 7x+8y=4.15
(2) 5x+3y=1.77

Choose a variable to eliminate. I’ll eliminate X first as an example. To eliminate a variable, you must have the same coefficient beside the variable for both equations.

Equation 1 now becomes:

(3) 35x+40y=20.75

Equation 2 now becomes:

(4) 35x+21y=12.39

Now that you have 35 as a coefficient for X in both equations, you can subtract the two equations to officially eliminate it!

(3)-(4)

19y=8.36
y=0.44

Now that you have the value of Y, substitute that value into either one of the equations to get X.

Substitute y=0.44 in (1)

7x+8(0.44)=4.15
7x+3.52=4.15
7x=0.63
x=0.09

Therefore, the cost per pencil is $0.09/pencil and the cost per notebook is $0.44/notebook.

Almost done lol...

To find the cost of 16 pencils, multiply 0.09*16. That gives you $1.44, which will be the cost of 16 pencils.
The cost of 10 notebooks is 0.44*10, which gives you $4.40. That’s the cost of 10 notebooks.

To find the total price, add these values together!

1.44+4.40=5.84

Therefore, the cost of 16 pencils and 10 notebooks is $5.84.

Hope that helps シ