Question

What is the 7th term of the geometric sequence where a1 = –4 and a5 = –1,024

Answer 1

The process: A geometric sequence means that the general term is given by the following expression for some constant \(C\). \[\Huge a_n=a_1 \cdot C^{n-1}\] Use this information to reason out the value of \(C\), and plug in \(n=7\).

Answer 2

that doesnt make sense to me, can you explain

Answer 3

Here, you are given \(a_1=-4\), so the terms are as follows, using the formula.\[a_1,a_2,a_3,a_4,\ldots=a_1,Ca_1,C^2a_1,C3a_1,\cdots=^-4,-4C,-4C^2,-4C^3,\ldots\]See how we multiply on the factor \(C\) each time? We can figure out that value, and find out \(a_7=C^6a_1\). (Note: click on any equation to make it bigger).

Answer 4

Correction: \(C^3a_1\).