Question

Identify the formula for the $n^{th}$ term of the sequence $54,18,\mathrm{6....}$

• A. $54{\left(\frac{1}{3}\right)}^{n-1}$
• B. $6{\left(\frac{1}{3}\right)}^{n-1}$
• C. $3{\left(\frac{1}{3}\right)}^n$
• D. $54{\left(\frac{1}{3}\right)}^n$

Answer 1

Answer: (A)

$54{\left(\frac{1}{3}\right)}^{n-1}$

Given series is $54,18,6,....$

Here first term $=a=54$, common ratio $=$ $\frac{1}{3}$
We know the formula for $n^{th}$ term,
$a_n=a{r}^{n-1}$
$a_n=54{\left(\frac{1}{3}\right)}^{n-1}$