Final answer:
To find the first term of a geometric sequence with the formula gn = 128 (1/2)^n, we substitute n with 1 to get g1 = 128 (1/2)^1 = 64. The first term, g1, is 64, but this is not listed in the options which may imply there has been a misunderstanding or typo in the question.
option a is the correct
Step-by-step explanation:
The question involves a geometric sequence where the nth term is given by gn = 128 (1/2)^n. To find the first term g1, also known as gg, we need to substitute n with 1 into the formula.
Substituting n=1, we get:
g1 = 128 (1/2)^1 = 128 × 1/2 = 64. Thus, the first term in the sequence is 64. However, this value is not among the provided options. It seems there is either a misunderstanding of the question or a typo. It is important to confirm the notation used in the sequence. If gn represents the nth term, then this procedure is correct. If it follows a different notation, we must have the correct information to answer accurately.
Typically, in a geometric sequence, the first term is denoted by a1, and the common ratio by r. Assuming that gn represents the nth term in standard notation, and that the common ratio is 1/2, none of the provided options match the correctly computed first term.