What is the 6th term in the geometric series 256+128+64
To find the 6th term in the geometric series 256, 128, 64, we need to first identify the common ratio.
The common ratio between each term is found by dividing any term by the previous term.
The first term (a) is 256 and the second term (b) is 128.
Common ratio (r) = b/a = 128/256 = 0.5
To find the 6th term, we can use the formula:
𝑎𝑛 = 𝑎 * 𝑟^(𝑛−1)
where a is the first term, r is the common ratio, and n is the position of the term.
Substituting the values into the formula:
𝑎𝑛 = 256 * 0.5^(6−1)
𝑎𝑛 = 256 * 0.5^5
𝑎𝑛 = 256 * 0.03125
𝑎𝑛 = 8
Therefore, the 6th term in the geometric series 256, 128, 64 is 8.