Question

What is the 10th term of the geometric sequence 3, 12, 48, 192,...?​

Answer 1

Given :

a=3

ar=12

ar²=48

r=12/3=48/12=4

To find :

10th term of given sequence

Solution:

we know,

$T_n=a\times{r}^{n-1}\\\\T_{10}=3\times{4}^{9}\\\\T_{10}=3\times262144\\\\T_{10}=786432\\\\\\\\\\\underline{\boxed{\sf{T_{10}=786432 }}}$

Answer 2

The 10th term of the geometric sequence is 7,86,432.

Step-by-step explanation:

• A geometric sequence is one in which “a” represents an initial value and "r" represents a common factor between words.
• In response to the query, we can predict that the $n^{th}$ term will take the form as $ar^{n-1}$ and so the tenth term would be $ar^{9}$.

The first term is 3 so, $a=3$

In order to find "r", we just need to divide a term by the term that is before it.

∴ $r=\frac{ar}{a}$

∴ $r=\frac{12}{3}$

∴ $r=4$

Hence, the $10^{th}$ term would be: $3\times 4^{9}=7,86,432$