Geometric Progression(GP): Formulae based
Example 4
Ex 8.2, 1
Example 5 Important
Ex 8.2, 5 (a)
Ex 8.2, 2
Example 6
Ex 8.2, 4
Ex 8.2, 3 Important
Ex 8.2, 17 Important
Example 7 Important
Ex 8.2, 7 Important
Ex 8.2, 10
Ex 8.2, 9 Important
Ex 8.2, 11 Important
Ex 8.2, 8
Ex 8.2, 19
Ex 8.2, 20 You are here
Example 8
Ex 8.2, 13
Ex 8.2, 15
Ex 8.2, 16 Important
Ex 8.2, 21
Ex 8.2, 14 Important
Misc 3
Misc 2
Example 9 Important
Ex 8.2, 12
Example 10 Important
Ex 8.2, 18 Important
Misc 11 (i) Important
Misc 5
Misc 1 Important
Geometric Progression(GP): Formulae based
Last updated at April 16, 2024 by Teachoo
Ex 8.2, 20 Show that the products of the corresponding terms of the sequences a, ar, ar2, ar3… arn – 1 & A, AR, AR2, AR3…… ARn - 1 form a G.P, and find the common ratio. 1st sequence is a, ar, ar2, ar3… arn – 1 2nd sequence is A, AR, AR2, AR3…… ARn – 1 Let P = Product of corresponding terms of 1st & 2nd sequence = a × A , ar × AR , ar2 × AR2 , … , arn–1 × ARn–1 = aA , arAR , ar2AR2 , …, aA(rn–1Rn–1 ) P = aA, arAR, ar2AR2, …aA(rn–1Rn–1 ) Now, in aA, arAR, ar2AR2, …aA(rn–1Rn–1 ) 𝑎𝑟𝐴𝑅/𝑎𝐴 = rR & 𝑎𝑟2𝐴𝑅2/𝑎𝑟𝐴𝑅 = Rr Thus, (𝑆𝑒𝑐𝑜𝑛𝑑 𝑡𝑒𝑟𝑚)/(𝐹𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚) = (𝑇ℎ𝑖𝑟𝑑 𝑡𝑒𝑟𝑚)/(𝑆𝑒𝑐𝑜𝑛𝑑 𝑡𝑒𝑟𝑚) , i.e. common ratio is same Thus, it is a G.P Common ratio = r = (𝑠𝑒𝑐𝑜𝑛𝑑 𝑡𝑒𝑟𝑚 )/(𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚 ) = 𝑎𝑟𝐴𝑅/𝑎𝐴 = rR