The answer is 9. because... (8+9) + 32= 49
Answer:
the common ratio is either 2 or -2.
the sum of the first 7 terms is then either 765 or 255
Step-by-step explanation:
a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.
so,
a1
a2 = a1×f
a3 = a2×f = a1×f²
a4 = a3×f = a1×f³
the problem description here tells us
a3 = 4×a1
and from above we know a3 = a1×f².
so, f² = 4
and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).
again, the problem description tells us
a2 + a4 = 30
a1×f + a1×f³ = 30
for f = 2
a1×2 + a1×2³ = 30
2a1 + 8a1 = 30
10a1 = 30
a1 = 3
for f = -2
a1×-2 + a1×(-2)³ = 30
-10a1 = 30
a1 = -3
the sum of the first n terms of a geometric sequence is
sn = a1×(1 - f^(n+1))/(1-f) for f <>1
so, for f = 2
s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765
for f = -2
s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =
= -1×-255 = 255
The average between 12.00 and 15.00 seconds
can be defined in a few different ways.
Way #1: (speed)
Average speed =
(1/2) (the speed at 12 seconds + the speed at 15 seconds) .
Way #2: (speed)
Average speed =
(1/3) (the distance covered between 12.00 and 15.00 seconds)
Way #3: (velocity)
Average velocity =
(1/3) (distance between location at 12 sec and location at 15 sec)
in the direction from location at 12 sec to location at 15 sec.
That's the best we can do with the combination of given and
not given information in the question.
It is more than just a quadrilateral. In fact it is going to be hard to pick.
These facts suit a square, a rectangle, a rhombus, and a parallelogram. And the above statement is true, but maybe a little harder to prove than the converse of the statement, which is the usual one you find.
The converse is "If you have a parallelagram, the diagonals bisect each other."
You might think a trapezoid deserves some mention. The diagonals of a trapezoid do not bisect each other.
