# How do you find the explicit formula for the following sequence 3, 6, 12, 24, 48, . . .?

${n}^{t h}$ term of the geometric sequence is given by $3 \cdot {2}^{n - 1}$
$3 , 6 , 12 , 24 , 48 , . . .$ is a geometric sequence with $3$ as first term and subsequent terms being multiplied by $2$. In a geometric sequence with $a$ as first term and subsequent terms being multiplied by $r$, ${n}^{t h}$ term is given by
$a \cdot {r}^{n - 1}$ and hence ${n}^{t h}$ term of the geometric sequence is given by
$3 \cdot {2}^{n - 1}$