Problem

Find four numbers forming a geometric progression…

03:09

Problem 20 Easy Difficulty

Show that the products of the corresponding terms of the sequences $a, a r, a r^{2}$, $\ldots a r^{n-1}$ and $\mathrm{A}, \mathrm{AR}, \mathrm{AR}^{2}, \ldots \mathrm{AR}^{n-1}$ form a G.P, and find the common ratio.

Answer

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Precalculus

NCERT Class 11 - Math

Chapter 9

Sequences and Series

Section 3

Series

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Video Transcript

So we have problem number 20. Which says that Sure that the products of the corresponding terms from a GP and the damn sad. A. R. He has choir up to a R. A H. To the power and minus one second sequence is a. They are a R squared up to eight hours with power and minus one. So we have to first find the that the multiplication the product forms GP and find the common issue of that G. P. So first of all, let us multiply it corresponding terms like this with this E comma A R R comma E A R Squire are square A added to the power in minus when added to power and minus one. Okay, so if this is to be a G. P we have to get there common ratio. So let us divide A by a. We'll be getting our. Uh huh. Similarly if you divide this term A R squared R squared by E A R R. We'll be getting uh So we can see that these are coming to the coming to bit equal, which means a two by a one. That is second term by first term, equal to a third term by a second term, equal accommodation equal to R. R. So this forms a G. P. With common ratio uh and to our.

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