Option B: 1088 is the next term in the geometric sequence.
Explanation:
The sequence is 
We need to determine the next term.
To determine the next term, let us find the common ratio between the terms.
Thus, the common ratio is 
And the given sequence is a geometric sequence.
To determine the next term in a geometric sequence, we always multiply the common ratio to the current term.
Hence, the current term is 272 and the common ratio is 4.
Next term = Current term × Common ratio
Thus, the next term of the geometric sequence is 1088
Therefore, Option B is the correct answer.
Answer:
Graph C and Graph A
Step-by-step explanation:
Answer:
Graph (C)
Step-by-step explanation:
If Bob traveled 'y' miles in 'x' hours,
Distance traveled ∝ Time taken to cover the distance
y ∝ x
y = mx
Here, m = proportionality constant Or slope of the line
Since, Bob covered 45 miles in 1.5 hours,
m = 
m = 30 miles per hour
From the given graphs,
Graph (C) shows the slope = 
= 
= 30 miles per hour
Therefore, Graph (C) will show the relationship.
Q1: y = -3/2x +1
Q2: The graph changes vertically from -1 to 3 (4 units) at the same time it changes horizontally from -4 to 1/2 (4.5 units). The rate of change is 4/4.5 = 8/9 ≈ 0.8889. The closest answer selection is 9/10.
Q3: x=-2
Q4: The graph changes vertically by -4 at the same time it changes horizontally by +1. The slope is 4/-1 = -4. The y-intercept is +1, so the equation is
.. y = -4x +1
Q5: After the same pattern as above,
.. y = 5/2*x +5
Answer:
S45 = -3.6875×10^20
Step-by-step explanation:
Given the geometric series
-0.5+1.5-4.5+...
The common ratio r = +1.5/-0.5 = -4.5/1.5 = -3
Since the common ratio is less than 1
Sum of geometric series will be calculated using the formula below:
Sn = a(1-r^n)/1-r
Where n is the number of terms = 45
a is the first term of the series = -0.5
r is the common ratio = -3
Substituting this values into the formula
S45 = -0.5{1-(-3)^45}/1-(-3)
S45 = -0.5{1-(-3)^45}/4
S45 = -0.5{1-(-2.95×10²¹}/4
S45 = -0.5(1+2.95×10²¹)/4
S45 = (-0.5-1.47×10²¹)/4
S45 = -1.475×10²¹/4
S45 = -3.6875×10^20
