The second and the fifth terms of a geometric sequence are 16 and 1024...

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The second and the fifth terms of a geometric sequence are $16$ and $1024$, respectively. Which term of this sequence is $4,096$?

Can someone show me how to do this? I did:

$$ar^4 = 1024$$

$$ar=16$$

$$r^3=64$$

$$r=4$$

So that makes $a_1=4$ as well

what do I do now?

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1 Answer

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Now you need to just find an integer $n$ such that $ar^{(n-1)} = 4096$. This n will be the answer.
From what you have so far, it's obvious that this $n$ is $n=6$. In other words the 6th term is $4096$.

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