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
4x (4 peaches) = 4y (4.96$)
x (4/4 peaches=1) = y (4.96$ / 4 = 1.24$)
y f(x) = 1.24$
Answer:
Area = 960 cm^2
Step-by-step explanation:
Perimeter (P) = 2 (l + w)
P = 2l + 2w
Let the length be 5x
Let the width be 3x
From the question, P = 128.
Therefore:
128 = 2l + 2w
Divide both sides by 2.
l + w = 64
Recall we said:
l = 5x
w = 3x
So then:
5x + 3x = 64
8x = 64
Divide both sides by 8
x = 64/8
x = 8.
Since x = 8
Length = 5x = 5*8 = 40cm
Width =3x = 3 * 8 = 24cm
Area of a RECTANGLE:
Area = length * width
Area = 40 * 24
Area = 960 cm^2
The answer to your question is X= 11
