Let's find the explicit rule for the given arithmetic sequence following a step-by-step approach:
1. Identify the first term:
The first term [tex]\( f(1) \)[/tex] of the sequence is 2.7.
2. Determine the common difference:
To find the common difference, subtract the first term from the second term.
[tex]\[
\text{Common difference} = 4.3 - 2.7 = 1.6
\][/tex]
3. Form the explicit formula:
The general formula for an arithmetic sequence is:
[tex]\[
f(n) = \text{first term} + (n - 1) \times \text{common difference}
\][/tex]
Substituting the known values:
[tex]\[
f(n) = 2.7 + (n - 1) \times 1.6
\][/tex]
Therefore, the explicit rule for the arithmetic sequence is:
[tex]\[
f(n) = 2.7 + 1.6(n - 1)
\][/tex]
So, the correct answer is option [tex]\( \text{d} \)[/tex]. [tex]\( f(n) = 2.7 + 1.6(n-1) \)[/tex].
