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
Your answer is B. 2
This is because to rationalise the denominator, we need to multiply it by (3 - √7), so we get:
(3 + √7)(3 - √7)
3 × 3 = 9
3 × √7 = 3√7
3 × -√7 = -3√7
√7 × -√7 = -7
So all in all you get 9 - 7 which is 2.
I hope this helps!
Z=118 as vertically opposite angles are the same
x= (8x-50)
Answer:
x=0, - 9
Step-by-step explanation:
x^2+9x=0
x(x+9)=0
x=0 or x=-9
Tom is correct, and Dan is wrong. A quadrilateral is a closed figure with four sides, for example, like a kite. A parallelogram is a four sided rectangular figure with opposite sides that are parallel.
