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:
3:5
Step-by-step explanation:
5a + 3b = 6b
5a=6b-3b
5a=3b
a/b= 3/5
a:b=3:5
 
        
             
        
        
        
Answer: -5 2/3
Step-by-step explanation:
 
        
             
        
        
        
Answer:
2 Answers By Expert Tutors
Consider as an example a box of length L, width W, and height H. If all linear dimension are doubled the area becomes 4 (22) times the original
Step-by-step explanation:
google 
 
        
             
        
        
        
How much he lost: 1/3
How much he has left: 2/3
 Hope it helps!