Answer:
3) 2/3
4) an = 162·(1/3)^(n-1)
Step-by-step explanation:
3) A geometric sequence has a common ratio between adjacent terms. Here, that ratio is ...
r = 54/162 = 18/54 = 6/18 = 1/3
Then the next two terms can be found by multiplying by the common ratio:
6 · 1/3 = 2
2 · 1/3 = 2/3 . . . . . the sixth term
____
4) The generic expression for the n-th term of a geometric sequence with first term a1 and common ratio r is ...
an = a1·r^(n-1)
We can put in the numbers for a1 and r, and we have ...
an = 162·(1/3)^(n-1)
