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:
idc its 12
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
1 2 3 4 5 6 7 8 quick math
subtract 3 from 23 and u will get 20 then divide 2 by 2 and 2 by 20
x= 10
Answer:
<em>There are 21 jelly beans in the jar.</em>
Step-by-step explanation:
Suppose, the number of jelly beans in the jar is 
Two were off by 2, two were off by 3, two were off by 4. That means, the six guessed number will be: 
Given that, Alice guessed 25; Betty, 18; Clare, 23; Dotty, 19; Edith, 24; and Fran, 17.
So, the sum of all six guessed number will be: 
Thus, the equation will be..........

So, the number of jelly beans in the jar is 21.