Question

The first difference of a sequence is 1, 4, 7, 10, 13…

1) Find the first 6 terms when the first term of the original sequence is 4.

2) Find the first 6 terms when the sum of the first two terms of the original sequence is 7.

3) Find the first 6 terms when the fifth term in the original sequence is 25.

Answer 1

1) {4, 5, 9, 16, 26, 39}

2) {3, 4, 8, 15, 25, 38}

3) {3, 4, 8, 15, 25, 38}

Explanation:

Hi!

Let's call the sequence {x₁, x₂, x₃, etc}

The information you have is the difference between to consecutive terms:

`x_2-x_1= 1\\x_3-x_2= 4\\x_4-x_3= 7\\x_4-x_5= 10\\x_6-x_5= 13`

1) Data: x₁=4, then to get x₂ you sum 1, and get x₂=5. Then to get x₃ you sum 4, and get x₃=9, and so on. Result: {4, 5, 9, 16, 26, 39}

2) Data: x₁ + x₂ = 7. You know that x₂ = x₁ + 1. Then:

`x_1+x_2 = x_1 +x_1 +1= 2x_1+1=7\\x_1=3\\x_2= x_1 +1 = 3+1=4`

If you continue the same process as in 1), you get {3, 4, 8, 15, 25, 38}

3) Data: x₅ = 25. If you look at the result in 2), you see that x₅ = 25 there!

So the sequence in this case is the same as before {3, 4, 8, 15, 25, 38}