Question

1. What is the fourth term of the sequence an=an - 1 + 11 when a1 = 42. complete the sequence: 5,9,13,17, a5, a63. Complete the sequence : 128, 64, a3, 16, 8, a6, 2

Answer 1

1. What is the fourth term of the sequence an=an - 1 + 11 when a1 = 4

we have the equation

`a_(n=a(n-1))+11`

Find the second term

For n=2

`\begin{gathered} a_(2=a(2-1))+11 \\ a_(2=a1+11) \\ \text{substitute the given value} \\ a_(2=4+11) \\ a_(2=15) \end{gathered}`

Find the third term

For n=3

`\begin{gathered} a_(3=a2+11) \\ a_(3=15+11) \\ a_(3=26) \end{gathered}`

Find the fourth term

For n=4

`\begin{gathered} a_(4=a3+11) \\ a_(4=26+11) \\ a_(4=37) \end{gathered}`

therefore

the fourth term is 37

2. complete the sequence: 5,9,13,17, a5, a6

we have

a1=5

a2=9

a3=13

a4=17

Find the value of the common difference d

a2-a1=9-5=4

a3-a2=13-9=4

a4-a3=17-13=4

so

the value of d=4

we have that

a2=a1+d

a3=a2+d

a4=a3+d

a5=a4+d

substitute

a5=17+4=21

a6=a5+d

a6=21+4=25

therefore

a5=21 and a6=25

3. Complete the sequence : 128, 64, a3, 16, 8, a6, 2​

Its not an arithmetic sequence

verify if the sequence its a geoemetric sequence

a1=128

a2=64

a2/a1=64/128=0.5

the common ratio is 0.5

so

a3=a2*r

a3=64*(0.5)=32

a4=16

a5=8

a6=a5*0.5

a6=8*0.5=4

a7=2

therefore

a3=32 and a6=4