Position
1 2 3 4 5 n
Value of term
2 12 17 22 27

Note: It seems the first term of your sequence is 7 instead of 2. So, I am assuming you meant the sequence such as;

7, 12, 17, 22, 27

The expression for the nth term of the givens sequence is:

Step-by-step explanation:

Given the sequence

7, 12, 17, 22, 27

Here, the first element of the sequence is:

An arithmetic sequence has a constant difference 'd' and is defined by  

computing the differences of all the adjacent terms

The difference between all the adjacent terms is the same and equal to

so substituting d = 5 and in the nth term to determine the expression

Therefore, the expression for the nth term of the givens sequence is:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form