1. What is the fourth term of the sequence an=an - 1 + 11 when a1 = 4
we have the equation
[tex]a_{n=a(n-1)}+11[/tex]Find the second term
For n=2
[tex]\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}[/tex]Find the third term
For n=3
[tex]\begin{gathered} a_{3=a2+11} \\ a_{3=15+11} \\ a_{3=26} \end{gathered}[/tex]Find the fourth term
For n=4
[tex]\begin{gathered} a_{4=a3+11} \\ a_{4=26+11} \\ a_{4=37} \end{gathered}[/tex]therefore
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
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
