Can you solve in english

The sum formula is $S_n = \frac{n}{2}(a + l)$.

Divide both sides by 12:

The number of terms is 21.

The formula for the last term is $l = a + (n-1)d$.

Subtract 4 from both sides:

Divide both sides by 20:

Simplify the fraction:

The common difference is $\boxed{\frac{4}{5}}$ or $\boxed{0.8}$.

The growth factor per 20-minute period is $1 + 0.60 = 1.6$.
The exponential growth formula is $P_t = P_0 \times (\text{growth factor})^k$, where $k$ is the number of 20-minute periods.

Divide both sides by 2500:

To find $k$, we can test powers of 1.6:
$1.6^1 = 1.6$
$1.6^2 = 2.56$
$1.6^3 = 4.096$
$1.6^4 = 6.5536$
Thus, $k = 4$.

Since $k$ is the number of 20-minute periods, the total time is $k \times 20$ minutes.
Time = $4 \times 20 = 80$ minutes.
It will take $\boxed{80 \text{ minutes}}$ to reach 16384 bacteria.