To find the number of terms in the geometric sequence 16, 8, 4, 2, 1/16, we start by identifying the first term and the common ratio of the sequence.
The first term (a) is 16. To find the common ratio (r), we can divide the second term by the first term. So:
r = 8 / 16 = 0.5
This shows that each term is obtained by multiplying the previous term by 0.5. Now, let’s identify how many times we can keep multiplying until we reach 1/16.
The terms can also be expressed as:
- 1st term: 16 = 16 x (0.5)^0
- 2nd term: 8 = 16 x (0.5)^1
- 3rd term: 4 = 16 x (0.5)^2
- 4th term: 2 = 16 x (0.5)^3
- 5th term: 1 = 16 x (0.5)^4
- 6th term: 0.5 = 16 x (0.5)^5
- 7th term: 0.25 = 16 x (0.5)^6
- 8th term: 0.125 = 16 x (0.5)^7
- 9th term: 0.0625 = 16 x (0.5)^8
- 10th term: 1/16 = 16 x (0.5)^9
As we can see, the term 1/16 corresponds to the 10th term. Thus, there are a total of 10 terms in this geometric sequence.