Question

13 multiple-choice question for the sequence: 8, 20, 50, 125,... what is the proper explicit formula? $a_n = 8 + 2.5(n - 1)$ $a_n = 8 cdot 2.5(n - 1)$ $a_n = 2.5 cdot 8^{n - 1}$ $a_n = 8 cdot 2.5^{n - 1}$ rewatch submit

Explanation:

Step1: Identify Sequence Type

Check if the sequence is geometric (ratio between terms constant).
$\frac{20}{8} = 2.5$, $\frac{50}{20} = 2.5$, $\frac{125}{50} = 2.5$. So, geometric sequence with first term $a_1 = 8$ and common ratio $r = 2.5$.

Step2: Geometric Sequence Formula

The explicit formula for a geometric sequence is $a_n = a_1 \cdot r^{n - 1}$. Substituting $a_1 = 8$ and $r = 2.5$, we get $a_n = 8 \cdot 2.5^{n - 1}$.

Step3: Verify Options

• Option 1: Arithmetic (adds 2.5), but sequence is geometric. Eliminate.
• Option 2: Incorrect format (multiplies by $2.5(n - 1)$ instead of exponent). Eliminate.
• Option 3: Swaps $a_1$ and $r$. Eliminate.
• Option 4: Matches $a_n = 8 \cdot 2.5^{n - 1}$.

Answer:

D. $a_n = 8 \cdot 2.5^{n - 1}$ (assuming the last option is D; if options are labeled differently, the correct formula is $a_n = 8 \cdot 2.5^{n - 1}$)