Question

What is the 6th term of the geometric sequence where a1 = 1,024 and a4 = −16?

Answer 1

To find the 6th term of the geometric sequence, we need to determine the common ratio 'r' first. We can do this by dividing any term of the sequence by the preceding term. Using a1 = 1,024 and a4 = -16, we can say that: r = a2/a1 = a3/a2 = a4/a3 r = (-16)/(-64) = 1/4 Now we can use the a6 formula: a6 = a1 * r^(n-1) a6 = 1,024 * (1/4)^5 a6 = 1,024 * 1/1024 a6 = 1 Therefore, the 6th term of the geometric sequence is 1.