Answer:
[tex]a_n=a_{n-1}+3 [/tex] when n is even
[tex]a_n=a_{n-1}-2[/tex] when n is odd
Step-by-step explanation:
We are given that a sequence
6,9,7,10,8
We have to make  conjecture about the next item in the sequence.
We have
[tex]a_1=6[/tex]
[tex]a_2=9[/tex]
[tex]a_3=7[/tex]
[tex]a_4=10[/tex]
[tex]a_5=8[/tex]
[tex]a_2-a_1=9-6=3[/tex]
[tex]a_3-a_2=7-9=-2[/tex]
[tex]a_4-a-3=10-7=3[/tex]
[tex]a_5-a_4=8-10=-2[/tex]
We can see that the second term is increase by 3 from first term, third decrease by 2 from second term,fourth term increase by 3 from third term, fifth term decrease by 2 from fourth term.
[tex]a_n=a_{n-1}+3 [/tex] when n is even
[tex]a_n=a_{n-1}-2[/tex] when n is odd
