The formula for any geometric sequence is a n = a 1 · r n - 1 , where a n represents the value of the nth term, a 1 represents the value of the first term, r represents the common ratio, and n represents the term number. What is the formula for the geometric sequence 4, 8, 16, 32, ...? an = 32 · 2n - 1
an = 2 · 4n - 1
an = 4 · (1/2)n - 1
an = 4 · 2n - 1

Step-by-step explanation:instead, try making the subscripts and superscripts stand out:

                         n-1

a    =  a         * r

 n         n-1

Believe me, it's worth the extra work to do this!!

Given the sequence   -3, -6, -12, -24, you can easily see that the first term,

a         is    -3.  The common factor is 2.  Note how (-3)*2=-6, and so on.

  1

So, a       = -3 and r=2.

        1

So the formula for this geometric sequence is  

                  n-1

a     =  -3*2

  n

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.