What is the nth term rule of the quadratic sequence below? 7, 14, 23, 34, 47, 62, 79

Tn = Tn-1 + 2(n-1) + 5

Kindly note that Tn-1 means T subscript n-1

Step-by-step explanation:

Here, we want an expression for the nth term.

First term is 7

Then first common difference is 7

second common difference is 7 + 2

Third common difference is 9 + 2

So within the common differences, the nth term is 7 + (n-1) 2

Now, the nth term of the series would be;

Tn = Tn-1 + 7 + 2(n-1)

Tn = Tn-1 + 7 + 2n -2

Tn = Tn-1 + 2n + 5

Now there is a fix to this,

n for the term is not the same n for the common difference.

the 7th term works with the 6th common. difference, while the 8th term work for the 7th common difference.

So we might need to rewrite the final expression as follows;

Tn = Tn-1 + 2(n-1) + 5

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

my dear correct answer is option number 3