Explicit Recursive Equations

f(n) = f(n-1) + 5
What does f(n-1) represent?

• The desired number in a sequence

• The previous number in a sequence

Which of the following equations is recursive?

• f(n) = 3n+2

• f(n) = f(n-1) + 3

  f(0)=2

Which equation would be best for helping you find the 72^nd term?

• f(n) = 4(2)ⁿ⁺⁵

• f(n) = f(n-1) * 2

  f(0)=6

What is the explicit rule for the sequence:
11, 22, 44, 88...

• a_n = 2(11)^n-1

• a_n = 11x2

• a_n = 11(2)^n-1

• a_n+1 = a_{n *} 2;  a₁ = 11

Write the explicit rule in recursive form:  f_n = 11(2)^n-1

• f_n=f_{n-1 *} 11 ; f₁=2

• f_n=f_{n-1 *} 2 ; f₁=11

Find the recursive equation of the following sequence:

• t(1)=25; t (n+1)=t(n)*5

• t(1)=125; t (n+1)=t(n)(1/5)

• t(1)=25; t (n+1)=t(n)(1/5)

• t(1)=125; t (n+1)=t(n)*5

Find the recursive equation of this sequence

• t(1)=3; t (n+1)=t(n)*5

• t(1)=3; t (n+1)=t(n)*3

• t(1)=3; t (n+1)=t(n)*5ⁿ

• t(1)=3; t (n+1)=t(n)*3ⁿ

Given the recursive formula below, find the explicit formula. a₀ = 1 a_n = a_n-1 + 5

• f(n) = 6 + 5n

• f(n) = 1 + 5n

• f(n) = 5 + n

Given the recursive formula below, find the explicit formula. a₁ = 5 a_n = a_n-1 - 6

• f(n) = 5 - 6(n - 1)

• f(n) = 5 - 6n

• f(n) = -1 - 6n