Question

HELP

Nevin started a geometric sequence. The first four terms of his sequence are show below.
162,54,18,6, . . .
3.) What is the sixth therm of Nevin sequence? Show or explain how you got the answer.
4.) Write an expression that represents the ᵗʰ term of Nevin sequence.

Answer 1

3) 2/3

4) an = 162·(1/3)^(n-1)

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)