Recurrence Relations

Write down the first four terms of the sequence if a₁ = 1 and a_n+1 = 2a_n + 4.

• 0, 4, 12, 28

• 1, 4, 10, 18

• 1, 4, 12, 28

• 1, 6, 16, 36

• 6, 16, 34, 72

Given the recurrence relation

t_n+1 = 2t_n + 3 and t₃ = 25,

find t₆.

• 109

• 206

• 221

• 315

• 445

Given the recurrence relation

t_n+1 = 3t_n + 5 and t₄ = 200,

find the first term.

• 0

• 5

• 14

• 20

• 22

Find the recurrence relation that generates the sequence

11, 7, 3, –1, ...

• t_n+1 = t_n + 4, where t₁ = 11

• t_n+1 = t_n – 4, where t₁ = 11

• t_n+1 = –4t_n, where t₁ = 11

• t_n+1 = 2t_n + 2, where t₁ = 11

• t_n+1 = 2t_n – 15, where t1 = 11

A recurrence relation generates the arithmetic sequence

5, 9, 13, 17, ...

Find a rule for the nth term of the sequence.

• t_n = n + 4

• t_n = 4n – 3

• t_n = 4n + 1

• t_n = 4n + 5

• t_n = 5n + 4

If the 8th term of an arithmetic progression is –29, and the first term is 6, find the recurrence relation that describes the sequence.

• t_n+1 = –5t_n, where t₁ = 6

• t_n+1 = t_n + 5, where t₁ = 6

• t_n+1 = t_n + 13, where t₁ = 6

• t_n+1 = t_n – 5, where t₁ = 6

• t_n+1 = 7t_n – 11, where t₁ = 6

If the 6th term of an arithmetic progression is 22,

and the 13th term is 50,

find the recurrence relation that describes the sequence.

• t_n+1 = 4t_n, where t₁ = 2

• t_n+1 = t_n + 4, where t₁ = 2

• t_n+1 = t_n + 5, where t₁ = 2

• t_n+1 = t_n – 4, where t₁ = 2

• t_n+1 = 3t_n + 2, where t₁ = 2

Write the geometric sequence

10, –30, 90, –270, ...

as a recurrence relation.

• t_n+1 = –3t_n, where t₁ = 10

• t_n+1 = t_n – 3, where t₁ = 10

• t_n+1 = t_n + 10, where t₁ = 10

• t_n+1 = –3t_n – 3, where t₁ = 10

• t_n+1 = –3t_n + 10, where t₁ = 10

The 5th term in a geometric sequence is 2500 and the common ratio is 5.

Write the recurrence relation that describes this sequence.

• t_n+1 = 2t_n, where t₁ = 5

• t_n+1 = 4t_n, where t₁ = 5

• t_n+1 = 5t_n, where t₁ = 4

• t_n+1 = 5t_n + 5, where t₁ = 4

• t_n+1 = 5t_n + 4, where t₁ = 5

A recurrence relation generates the arithmetic sequence shown on the graph below.

Find the recurrence relation that generates this set of points.

• t_n+1 = 3t_n, where t₁ = –2

• t_n+1 = t_n – 3, where t₁ = –2

• t_n+1 = t_n + 3, where t₁ = –2

• t_n+1 = 2t_n + 5, where t₁ = –2

• t_n+1 = 3t_n – 3, where t₁ = –2