Question

Find a general term an for the sequence whose first four terms are given. 2, 4, 8, 16, ...

Answer 1

Answer:

  an = 2·2^(n-1)

Step-by-step explanation:

There are simple tests to determine whether a sequence is arithmetic or geometric. The test for an arithmetic sequence is to check to see if the differences between terms are the same. Here the differences are 2, 4, 8, so are not the same.

The test for a geometric sequence is to check to see if the ratios of terms are the same. Here, the ratios are ...

  4/2 = 2

  8/4 = 2

  16/8 = 2

These ratios are all the same (they are "common"), so the sequence is geometric.

The general term of a geometric sequence with first term a1 and common ratio r is ...

  an = a1·r^(n-1)

Filling in the values for this sequence, we find the general term to be ...

  an = 2·2^(n-1)