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rodrickahammonds
05.02.2020 •
Mathematics
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.
select one:
a. an = 2 • 3n - 1
b. an = 2 • (-3)n - 1
c. an = 2 • 3n
d. an = 2 • (-3)n + 1
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Ответ:
b. an = 2 • (-3)^(n - 1)
Step-by-step explanation:
Before we test a solution or two, we can easily discard most of them.
We see the values alternate of signs (-5 for the 2nd term and +162 for the 5th term)... so the progression factor has to be negative (in order to alternate sign). That already excludes answers A and C.
Normally, a geometric progression has the (n-1) exponent, not (n+1), so our chances seem to be better with B.
We can test both D and B with n = 2, to obtain -6
Let's test answer D before:
The result is -54, not -6... so it's not the right result.
Let's test answer B then:
Right! Let's verify with n=5 to get 162:
Confirmed, answer is B. an = 2 • (-3)^(n - 1)
Ответ:
For this picture below: Yes. The base and height can be determined for both triangles. Use the formula A = 1/2bh to find the area of each, then add them to get the area of the trapezoid. 10 + 15 = 25 in^2.