The sequence you’ve provided is a geometric sequence where each term is obtained by multiplying the previous term by a constant factor. Let’s break it down:
The first few terms are:
- 1st term: 4
- 2nd term: 8
- 3rd term: 16
- 4th term: 32
Looking closely, we can see that:
- 8 = 4 × 2
- 16 = 8 × 2
- 32 = 16 × 2
This shows that the common ratio (r) is 2. We can express the nth term of a geometric sequence using the formula:
nth term = a × r^(n-1)
where:
- a is the first term of the sequence (4 in this case)
- r is the common ratio (2)
- n is the term number
Now, to find the 20th term, we substitute the values:
20th term = 4 × 2^(20-1)
This simplifies to:
20th term = 4 × 2^19
Calculating 2^19, we find it equals 524288. Therefore:
20th term = 4 × 524288 = 2097152
So, the 20th term of the sequence is 2,097,152.