Q.The population of a town was 8,000 in 2020 and grows at a constant rate of 5% per year. Taking 2020 as the 1st term of a Geometric Progression, find the population in 2024 (to the nearest whole number).

A 5% annual growth means each year's population is $1.05$ times the previous year's — a GP with $r=1.05$; 2024 is the 5th term.

A constant percentage growth each year means the population forms a GP: $a=8000$ (population in 2020), $r=1.05$ (each year's population is $105\%$, i.e. $1.05$ times, the previous year's). Since 2020 is the 1st term, 2024 is the $(2024-2020+1)=5$th term.

Apply $T_n=ar^{n-1}$: $T_5=8000\times(1.05)^{4}$. Computing $(1.05)^2=1.1025$, so $(1.05)^4=(1.1025)^2=1.21550625$.

$T_5=8000\times1.21550625=9724.05$, which rounds to $9724$. …

A common error is miscounting the exponent by conflating "4 years elapsed since 2020" with an off-by-one slip elsewhere in the term count — 2024 is $4$ years after 2020, so the exponent on $r$ is correctly $4$ (i.e. $n-1=4$, giving $n=5$); always confirm $n-1$ …