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: 6 km to 22 km !
Step-by-step explanation:
the distances from the school mall to bus station could be, in the worst case, 14+8=22 km apart, and in the best case 14-8=6 km apart
so the range is 6 km to 22 km !
Answer:
Step-by-step explanation:
Total number of coins in the bag = 5 + 4 + 5 + 2 = 16 coins
Number of nickels in the bag = 4
We have to find the probability that Marissa draws a nickels from the bag.
Probability is defined as the ratio of Number of "Favorable Outcomes" to "Total number of possible outcomes"
In this case total number of possible outcomes is the total number of coins which is 16.
Favorable/Desires outcome is drawing a Nickle from the bag which are 4 in number. So, number of favorable outcomes is 4
Therefore, the probability that she will draw a nickel =
2x + 5 = 3x - 45 [alternate interior angles]
3x - 2x = 5 + 45
x = 50
4y - 1 + 2x + 5 = 180 [supplementaly angles]
4y + 2(50) + 4 = 180
4y + 100 = 176
4y = 76
y = 19
