Final answer:
The seventh term of the sequence 13, 52, 208, 832, ... is 53,248.
Step-by-step explanation:
The sequence given starts with 13 and each term is obtained by multiplying the previous term by 4. So, the common ratio in this geometric sequence is 4.
To find the seventh term, we can use the formula for the nth term of a geometric sequence:
an = a1 * r(n-1)
Here, a1 is the first term of the sequence (13) and r is the common ratio (4). Plugging in these values, we get:
a7 = 13 * 4(7-1)
a7 = 13 * 46
a7 = 13 * 4,096
a7 = 53,248
Therefore, the seventh term of the sequence is 53,248.