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Let g_1, g_2, g_3, be a geometric sequence. If g_{23} = 16 and g_{28} = 24, what is g_{43}?

 May 14, 2023
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The formula for a geometric sequence is an​=a1​rn−1, where a1​ is the first term, r is the common ratio, and n is the term number.

We know that g23​=16 and g28​=24. We can use these values to find the common ratio r.

g28​ = g23 r^{28 - 23} 24 = 16r^5 r^5 = 2 r = 2^(1/5)

Now that we know the common ratio, we can find g43​.

g43​=g23r^{43-23} g43 = 16*(2^{1/5})^(43-23) g43 = 16*(2^(1/5))^20 g43 = 16*2^4 g43 = 128

Therefore, g43​=128.

 May 14, 2023

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