Answer:
a. a[1] = 3; a[n] = 2a[n-1]
b. a[n] = 3·2^(n-1)
c. a[15] = 49,152
Step-by-step explanation:
Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.
The first term is 3, and the common ratio is 2.
<h3>(a)</h3>
The recursive rule is ...
a[1] = 3
a[n] = 2×a[n-1]
__
<h3>(b)</h3>
The explicit rule is ...
a[n] = a[1]×r^(n-1)
a[n] = 3×2^(n-1)
__
<h3>(c)</h3>
The 15th term is ...
a[15] = 3×2^(15-1) = 3×2^14
a[15] = 49,152
Answer:
y = 6x - 2
Step-by-step explanation:
slope intercept form is y = mx + b
m = slope
b = y-intercept
They give us the slope (m) which is 6 and the y-intercept (b) which is -2. PLug it into the equation
y = mx + b
y = 6x - 2
Answer:
33, 39, 45, 51
Step-by-step explanation:
The general term of an arithmetic sequence is given by the formula ...
an = a1 + d(n-1) . . . where a1 is the first term and d is the common difference
Comparing this formula to the one you are given, you see that ...
a1 = 33, d = 6
This means the first term is 33, and each successive term is 6 more than the previous one. The first 4 terms are ...
33, 39, 45, 51
Answer:
x = 50
Step-by-step explanation:
the word bisects means that it cuts in half (this is how I understand it, not the official definition :D)
so that means
Answer:
y = 2x + 3
Step-by-step explanation:
The y-intercept is clearly marked: it's b = 3 (or 0, 3).
Going from the point (-3, -3) to the point (0, 3),
x increases by 3 and y increases by 6. Thus, the slope of the line through these two points is m = rise / run = 6 / 3, or m = 2.
Starting with the slope-intercept form of the equation of a straight line:
y = mx + b, we substitute 2 for m and 3 for b, obtaining:
y = 2x + 3
