Find the 6th Term 3 , 12 , 48 , 192 ,

$3$ , $12$ , $48$ , $192$ ,

Step 1

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by $4$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 4$

Step 2

This is the form of a geometric sequence.

$a_{n} = a_{1} r^{n - 1}$

Step 3

Substitute in the values of $a_{1} = 3$ and $r = 4$ .

$a_{n} = 3 \cdot 4^{n - 1}$

Step 4

Substitute in the value of $n$ to find the $n$ th term.

$a_{6} = 3 \cdot 4^{(6) - 1}$

Step 5

Subtract $1$ from $6$ .

$a_{6} = 3 \cdot 4^{5}$

Step 6

Raise $4$ to the power of $5$ .

$a_{6} = 3 \cdot 1024$

Step 7

Multiply $3$ by $1024$ .

$a_{6} = 3072$

Find the 6th Term 3 , 12 , 48 , 192 ,

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