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
Answer:
-1 to the nearest whole number.
Step-by-step explanation:
(-0.3) ÷ (-0.2)+(-2.56)
Order of operations - the division is done first:
= 1.5 = (-2.56)
= 1.5 - 2.56
= -1.06.
Answer: 1.6
Step-by-step explanation:
This data set is 0,1,2,2,3. Thus, you can calculate the mean by doing (0+1+2+2+3)/5=1.6
Hope it helps <3
I can't see pictures, but to find the area of a triangle, you multiply the dimensions, as you would a rectangle, but divide the area by 2.
For example, the dimensions of a triangle are 4 and 6.
Multiply the two.
4x6=24.
But don't stop there. Divide 24 by 2.
24/2=12.
So the area of the example triangle is 12.
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hope it helps
