In this sequence, term number 1 has a value of 6,
term number 2 has a value of 12, term number 3 has
a value of 22, and so on:
6, 12, 22, 36, 54,
if n represents the term number, demonstrate that
the rule 2n + 4 will generate the sequence.

2n² + 4

Step-by-step explanation:

Let, ...... (1)

Now, sift the right hand side by one term and subtract from original equation (1).

Hence, we get  

(

⇒ tₙ = 6 + [ 6 + 10 + 14 + 18 + ........ up to (n-1)th term]  

Now, the sum within the bracket is an A.P. sum.

Hence, tₙ = 6+ []

               = 6+

               = 6+ 2(n²-1)

                = 2n² + 4

Therefore, the general term 2n² + 4 represent the sequence. (Answer)

the answer is 0.071

good luck! : d

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)