What's the next number 2 7 8 3 12 9

The correct answer is:

4.

Explanation:

Taking these numbers as groups of three, we have 2, 7, 8; 3, 12, 9.

In the first group, we can see that we first add 5 and then add 1.

The next group seems to start from the next consecutive number. That is, the first group starts with 2, and the next group starts with 3. The next terms in the second group are found by adding 5 to the second term of the first group (12 = 7+5) and then adding 1 to the third term of the first group (9=8+1); this is because we added 5 and added 1 previously.

Following this pattern, the next group of three would start from the next consecutive number up, 4. The next two terms would be 17 (12+5=17) and 10 (9+1=10).

The next term of teh sequence is .

Further explanation:

The sequence given in the question is .

The objective is to obtain the next term of the given sequence.

Group the terms of the given sequence. Consider that two groups are formed such that the terms are placed in group and the terms are place in group .

From the above two groups it is observed that first term of second group is obtained when the first term of group is increased by unit.

From group and group it is observed that the second term of the group is obtained when second term of group is increased by units.

From group and group it is observed that the thirdterm of the group is obtained when thirdterm of group is increased by unit.

Therefore, the relation between the elements of the two groups is given as follows:

Now, following the same pattern for the given sequence, the next term of sequence is obtained when the first term of group is increased by unit.

This implies that the next term of the given sequence is .

Therefore, the next term of the sequence is .

Learn more:

1.A problem on greatest integer function link

2.A problem to find radius and center of circle link  

3.A problem to determine intercepts of a line link  

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Sequence

Keywords: Series, sequence, logic, (2,7,8,3,12,9), groups, next term, successive term, mathematics, critical thinking, numbers, addition, subtraction, pattern, rule.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

if you are looking for the unit rate then the answer would be 9 because unit rate is distance divided by time.

step-by-step explanation: