Find the sum of the first five terms using the geometric series formula for the sequence left curly bracket 1 half comma space minus 1 comma 2 comma negative 4 comma... right curly bracket

Step-by-step explanation:

Given the geometric series:

To find:

Sum of series upto 5 terms using the geometric series formula = ?

Solution:

Formula for sum of a n terms of a geometric series is given as:

is the first term of the geometric series

is the common ratio between each term (2nd term divided by 1st term or 3rd term divided by 2nd term ..... ).

Here:

So, applying the formula for given values:

So, the answer is

366

step-by-step explanation:

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.