The first term of an Arithmetic progression is 3and the last term is 9, find the number of terms in the progression if the common difference is 3/2

n = 5 terms

Step-by-step explanation:

An = a1 + (n-1)d

9 = 3 + (n-1) 3/2

9 = 3 + 3/2n - 3/2

9 = 3/2 + 3/2n

9 - 3/2 = 3/2n

(15/2) / (3/2) = n

30/6 = n

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.

their is no graph showing

step-by-step explanation: