Answer:
Either (approximately ) or (approximately .)
Step-by-step explanation:
Let denote the first term of this geometric series, and let denote the common ratio of this geometric series.
The first five terms of this series would be:
First equation:
.
Second equation:
.
Rewrite and simplify the first equation.
.
Therefore, the first equation becomes:
..
Similarly, rewrite and simplify the second equation:
.
Therefore, the second equation becomes:
.
Take the quotient between these two equations:
.
Simplify and solve for :
.
.
Either or .
Assume that . Substitute back to either of the two original equations to show that .
Calculate the sum of the first five terms:
.
Similarly, assume that . Substitute back to either of the two original equations to show that .
Calculate the sum of the first five terms:
.
Answer:
(a) 8
(b) 16
(c) 24
(d) The ratios are the same
Step-by-step explanation:
(a) For inputs -5 and -4, the difference of outputs is ...
-3 -(-11) = 8
__
(b) For inputs 0 and 2, the difference of outputs is ...
45 -29 = 16
__
(c) For inputs -3 and 0, the difference of outputs is ...
29 -5 = 24
__
(d) The ratios of output difference over input difference are ...
8/1 = 16/2 = 24/3 = 8 . . . . . they are all the same
This is yet another confirmation that the slope of a line is the same everywhere, and over any interval.
Answer:
sure !
Step-by-step explanation: