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

Question

anonymous · Answer

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 $n=7$.

anonymous · Answer

that doesnt make sense to me, can you explain

anonymous · Answer

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).

anonymous · Answer

Correction: $C^3a_1$.

anonymous · Answer

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