Asequence is defined by this recursive function:

f(n) = (2.5) · f(n – 1); f(1) = 48

complete the table.
index function notation term value
1 f(1) = 48 48
2 f(2) = (2.5) · f(1) 120
3 f(3) = (2.5) · f(2) 300
4 f(4) = (2.5) · f(3)
5 f(5) = (2.5) · f(4)
6 f(6) = (2.5) · f(5)

to the nearest hundredth, the tenth term in the sequence is

Hello from MrBillDoesMath!

See the Discussion section below.

Discussion:

Study this pattern:

f(1) = 48

f(2) = 2.5 * 48

f(3) = 2.5 f(2) = 2.5 * ( 2.5 * 48 )   = 2.5^2 * 48

f(4) = 2.5 *  f(3) = 2.5 * (2.5^2 * 48) =   2.5^3 * 48

so generally

f(n) = 2.5^(n-1)  * 48,  n >=1

Therefore

f(4) = 2.5^3 * 48 = 750

f(5) = 2.5^4 * 48 = 1875

f(6) = 2.5^5 * 48 = 4687.5

f(10) = 2.5^9 * 48 =  183105.46875 which is 183105.47 to the nearest hundredth

Thank you,

MrB

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.