Question

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

Answer 1

11

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

Answer 2

`a_n=a_(n-1)+3` when n is even

`a_n=a_(n-1)-2` when n is odd

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