Question

Find the indicated terms of the sequence defined by each of the following recursive formulas:

Answer 1

a3 = −11 and an = 2an − 1 − 1

a2 = -11+1 = -10/2 =-5

a4 = 2(-11)-1 =-22-1=-23

a4 = −36 and an = 2 an − 1 − 4

a3 = -36+4 = -32/2=-16

a2 = -16+4=-12/2=-6

Answer 2

Answer:

1.

Given the recursive formula:

$a_3 = -11$ and

$a_n = 2a_{n-1} -1$

For n = 3:

$a_3=2a_2 -1$

Substitute $a_3 = -11$ we have;

$-11=2a_2 -1$

Add 1 to both sides we have;

$-10 = 2a_2$

Divide both sides by 2 we have;

$-5 = a_2$

or

$a_2 = -5$

For n = 4, we have;

$a_4=2a_3 -1$

Substitute $a_3 = -11$ we have;

$a_4 = 2 \cdot -11 -1 = -22-1 = -23$

⇒$a_4 = -23$

2.

Given:

$a_4 = -36$ and $a_n = 2a_{n-1} -4$

For n = 4, we have;

$a_4=2a_3 -4$

Substitute $a_4 = -36$ we have;

$-36 = 2a_3 -4$

Add 4 to both sides we have;

$-32 = 2a_3$

Divide both sides by 2 we have;

⇒$a_3 =-16$

For n = 3:

$a_3=2a_2 -4$

Substitute $a_3 = -16$ we have;

$-16=2a_2 -4$

Add 4 to both sides we have;

$-12 = 2a_2$

Divide both sides by 2 we have;

$-6 =a_2$

or

⇒$a_2 = -6$