Question

Make a conjecture about the next item in the sequence. 6, 9, 7, 10, 8

Answer 1

Answer:

$a_n=a_{n-1}+3$ when n is even

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

$a_1=6$

$a_2=9$

$a_3=7$

$a_4=10$

$a_5=8$

$a_2-a_1=9-6=3$

$a_3-a_2=7-9=-2$

$a_4-a-3=10-7=3$

$a_5-a_4=8-10=-2$

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.

$a_n=a_{n-1}+3$ when n is even

$a_n=a_{n-1}-2$ when n is odd

Answer 2

Answer:

11

Step-by-step explanation:

6 to 9 = +3,9 to 7= -2,7 to 10= +3,10 to 8 = -2 and the answer have to + 3 with 8