Final answer:
The fifth term of the geometric sequence with a starting term of 128 and a common ratio of ½ is found using the formula an = a1 × r(n-1), resulting in a fifth term of 8.
Step-by-step explanation:
The student has asked for a function of a geometric sequence with a starting term of 128 and a common ratio of ½. A geometric sequence can be defined by the formula an = a1 × r(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number. To find the fifth term, we would plug 5 into our formula as n.
To calculate the fifth term, we use the following steps:
- Identify the first term (a1) of the sequence, which is 128.
- Determine the common ratio (r), which is ½.
- Substitute these values into the formula along with the term number (n = 5): a5 = 128 × (½)(5-1).
- Simplify the expression: a5 = 128 × (½)4 = 128 × ¼ = 128 × 0.0625.
- Calculate the final value: a5 = 8.
Therefore, the fifth term of the geometric sequence is 8.