let n represent the position of a term in the arithemtic sequence

(-2,6,14,22,30,...)

a circle is a dilated by a scale factor of 2 to create a new circle.which of the following statements are true

I.the area of the new circle is 6times the area of the original circle
II.the area of the new circle is 4times the area of the original circle
III.the circumference of the new circle is 2times the circumference of the original circle.
IV.the circumference of the original circle
f)I and IV
G)IIand III
h)i and III
J)IIand IV

II and III

(IV is incomplete, but I assume false)

Tn = 8n-10

To find the position of a term in the arithmetic sequence (-2, 6, 14, 22, 30, ...), we can use the formula for the nth term of an arithmetic sequence.

The formula for the nth term of an arithmetic sequence is given by:

an = a1 + (n - 1)d

Where:
an is the nth term of the sequence,
a1 is the first term of the sequence, and
d is the common difference between consecutive terms.

In this case, the first term (a1) is -2, and the common difference (d) is 8. So, we can substitute these values into the formula:

an = -2 + (n - 1)8

Now, we can consider the position of a term in the sequence as n and express it in terms of the term itself:

n = (an - a1)/d + 1

Let's use this formula to find the position of a few terms.

For example, if we want to find the position of the term 14:

14 = (-2 + (n - 1)8)

Simplifying the equation:

14 = -2 + 8n - 8

Combine like terms:

14 = 6 + 8n

Subtract 6 from both sides:

8 = 8n

Divide both sides by 8:

1 = n

Thus, the term 14 is at the first position in the sequence. Similarly, we can use this formula to find the position of any other term in the sequence.