# MaTh

The 23rd term in a certain geometric sequence is 16 and the 28th term in the sequence is 24. What is the 43rd term?

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1. T43 = T28 + 15(T28-T23)/(28-23)
= 24 + 15(24-16)/5 = 48

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posted by Steve
2. I don't understand why so many people are getting 48, but that is not the answer. We know that in a geometric sequence, you multiply each term by a number to get your next term. So we know that we multiply our 23rd term by some number x 5 times to get our 28th number. So we know that 16 * x^5 = 24. All I did here was plug in the numbers. Therefore x^5 = 24/16 = 3/2, so x equals the fifth root of 3/2. We know that 24 * (fifth root of 3/2)^15 = T43 (T43 = 43rd term) . Simplifying this, we get T43 = 81.

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3. 81 is the correct answer, not 48

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posted by Girl
4. 81

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posted by Me

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