Q3 of 104 Page 468

If a, b, c are GP, then show that , are in AP.

To prove: , are in AP.


Given: a, b, c are in GP


Formula used: (i)


As, a, b, c are in GP


⇒


Taking log both side


⇒ log b – log a = log c – log b


⇒ 2log b = log a + log c


Dividing by log m


⇒


⇒


⇒


Whenever any number a,b,c are in AP then 2b = a+c, considering this and the above equation we can say that , are in AP


Hence proved


More from this chapter

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1

If p, q, r are in AP, then prove that pth, qth and rth terms of any GP are in GP.

 2

If a, b, c are in GP, then show that log an, log bn, log cn are in AP.

 4

Find the values of k for which k + 12, k – 6 and 3 are in GP.

 5

Three numbers are in AP, and their sum is 15. If 1, 4, 19 be added to them respectively, then they are in GP. Find the numbers.