Write an equation for the nth term of the geometric sequence $7,\ 28,\ 112,\ 448,\ ...$7, 28, 112, 448, ...​ . Then find $a_6$a6​​ .An equation for the nth term of the geometric sequence is $a_n=$an​=​ $\text{(}$(​ $\text{)}$)​ $^{n-1}$n−1​ .$a_6=$a6​=​

The given sequence is a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Step 1: Identify the common ratio The common ratio (r) can be found by dividing any term by the previous term. For example, 28/7 = 4, 112/28 = 4, 448/112 = 4. So, the common ratio (r) is 4.

Step 2: Write the nth term formula The nth term of a geometric sequence can be found using the formula: a_n = a * r^(n-1), where a is the first term and r is the common ratio.

So, for this sequence, the nth term formula is: a_n = 7 * 4^(n-1)

Step 3: Find the 6th term Substitute n = 6 into the formula: a_6 = 7 * 4^(6-1) = 7 * 4^5 = 7 * 1024 = 7168.

So, the 6th term of the sequence is 7168.