t₁ = 3

t_n = 2t_n-1

Knowing that the first terms is three (t₁ = 3), calculate the value of the second term (t₂)

Since we need to calculate t₂, substitute n = 2 into the second part of the recursive rule (t_n = 2t_n-1)

      t₍₂₎ = 2t_(2)-1

      t₂ = 2t₁                  (But it is known that t₁ = 3)

      t₂ = 2(3)

      t₂ = 6

Repeat this process to find t₃.

Knowing that the first two terms are three and six (t₁ = 3 and t₂ = 6, calculate the value of the third term (t₃)

Since we need to calculate t₃, substitute n = 3 into the second part of the recursive rule (t_n = 2t_n-1)

      t₍₃₎ = 2t_(3)-1

      t₃ = 2t₂                  (But it was calculated that t₂ = 6)

      t₃ = 2(6)

      t₃ = 12

Repeat this process to find t₄.

Knowing that the first three terms are three, six and twelve (t₁ = 3, t₂ = 6 and t₃ = 12), calculate the value of the fourth term (t₄)

Since we need to calculate t₄, substitute n = 4 into the second part of the recursive rule (t_n = 2t_n-1)

      t₍₄₎ = 2t_(4)-1

      t₄ = 2t₃                  (But it was calculated that t₃ = 0)

      t₄ = 2(12)

      t₄ = 24

Repeat this process to find as many terms as required.

Sequence: 3, 6, 12, 24, 48, 96, 192, . . .

Sequence: Starting with three, multiply each term of the sequence by two to determine the next term of the sequence.