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) {4, 5, 9, 16, 26, 39}2) {3, 4, 8, 15, 25, 38}3) {3, 4, 8, 15, 25, 38}Step-by-step explanation:Hi!Let's call the sequence {x₁, x₂, x₃, etc}The information you have is the difference between to consecutive terms:[tex]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[/tex]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:[tex]x_1+x_2 = x_1 +x_1 +1= 2x_1+1=7\\x_1=3\\x_2= x_1 +1 = 3+1=4[/tex]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}