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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
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 May 29, 2023 by Teachoo
Ex 8.2,6 For what values of x, the numbers (−2)/7, x, (−7)/2 are in G.P? Since (−2)/7, x, (−7)/2 are in GP So common ratio will be same Common ratio (r) = (𝑆𝑒𝑐𝑜𝑛𝑑 𝑡𝑒𝑟𝑚 )/(𝐹𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚) = 𝑥/((−2)/7) = 7𝑥/(−2) Also, Common ratio (r) = (𝑇ℎ𝑖𝑟𝑑 𝑡𝑒𝑟𝑚 )/(𝑆𝑒𝑐𝑜𝑛𝑑 𝑡𝑒𝑟𝑚) = ((−7)/2)/𝑥 = (−7)/2𝑥 From (1) & (2) 7𝑥/(−2) = (−7)/2𝑥 7x × 2x = (-7) × (-2) 14x2 = 14 x2 = 14/14 x2 = 1 x = ± √1 x = ±1 So, x = 1 or x = -1 GP is (−2)/7, x, (−7)/2 For x = 1, GP is (−2)/7, 1, (−7)/2 For x = –1, GP is (−2)/7, –1, (−7)/2 Hence possible numbers in GP are (−2)/7, 1, (−7)/2 or (−2)/7, –1, (−7)/2