Question

What are the missing values in the table representing the recursively defined geometric sequence f(x+1)=4(f(x))

X_f(x)
1_4
2_A
3_B
4_C
5_1,024

Answer 1

A=16

B=64

C=256

Explanation:

I did the assignment

Answer 2

Hence, the values of unknowns A,B and C are:

A=16

B=64

C=256

Explanation:

We are given a recursive defined geometric sequence f(x+1)=4(f(x))

X f(x)

1 4

2 A

3 B

4 C

5 1,024

When x=1,

we have f(x)=4.

when so,

f(2)=4f(1)=4×4=16.

Hence, when x=2 f(x)=16=A.

Similarly,

f(3)=4×f(2)

f(3)=4×16=64

Hence, when x=3 f(x)=64=B.

Similarly,

f(4)=4×f(3)=4×64=256

i..e when x=4 f(x)=256=C.

similarly,

f(5)=4×f(4)=4×256=1024

when x=5 f(x)=1024

Hence, the values of unknowns A,B and C are:

A=16

B=64

C=256