Question

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) 1, − 1/ 3 , 1 /9 , − 1 /27 , 1 /81 , . . .

Answer 1

9514 1404 393

Answer:

  a[n] = (-1/3)^(n -1)

Step-by-step explanation:

The terms have a common ratio of (-1/3)/(1) = -1/3. The general term for a geometric sequence with first term a1 and common ratio r is ...

  a[n] = a[1]×r^(n-1)

Here, a[1] = 1, so this is ...

  a[n] = (-1/3)^(n-1)