Recursive review

Determine the 3rd term of the sequence.

a₁=5

a_n= 2a_n-1 - 1

• 14

• 13

• 17

• 16

Answer explanation

f(1) = 3 <--- {starting value!}

f(n) =[f(n-1)]²  then, 

f(2) = [f(2-1)]²  

       = [f(1)]²   *f(1) = 3 

       = [3]²

          ^{= 9 **f(2) = 9}

^{f(2) = 9}                

f(3) = = [f(3-1)]²  

       = [f(2)]²   **f(2) = 9

       = [9]²

          ^{= 81}         

^{f(3) = 81} 

Answer explanation

f(1) = 2 & f(n) = 2 * f(n-1)

then, f(2) = 2 * f(2-1)

= 2 * f(1)

= 2 * 2

= 4

f(2) = 4

then, f(3) = 2 * f(3-1)

= 2 * f(2)

= 2 * 4

= 8

f(3) = 8

then, f(4) = 2 * f(4-1)

= 2 * f(3)

= 2 * 8

= 16

f(4) = 16

then, f(5) = 2 * f(5-1)

= 2 * f(4)

= 2 * 16

= 32

f(5) = 32

So the first five terms of the sequence will be 2, 4, 8, 16, 32.

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

• -16, -21, -26, -31
• 5, -11, -27, -43
• -16, -80, -500, -200
• -16, -11, -6, -1

Determine if the following sequence is arithmetic or geometric.

4, 9, 14, 19, 24, ...

• Arithmetic

• Geometric

Determine if the following sequence is arithmetic or geometric.

6, 12, 24, 48, 96, ...

• Arithmetic

• Geometric

Determine if the following sequence is arithmetic or geometric.

200, 100, 50, 25, ...

• Arithmetic

• Geometric

Determine if the following sequence is arithmetic or geometric.

15, 13, 11, 9, 7, ...

• Arithmetic

• Geometric

A formula that requires the computation of all previous terms to find the value of a_n.

• Explicit Formula

• Recursive Formula

• Arithmetic Formula

• Geometric Formula

Which symbol represents the first term of a sequence?

• d

• n

• f(n)

• f(1)