NTA Abhyas JEE Main2020MathematicsSequences and SeriesPractice

If a = 111 … . . 1 ⏟ 55 t i m e s , b = 1 + 10 + 10 2 + 10 3 + 10 4 and c = 1 + 10 5 + 10 10 + … . + 10 50 , then

Options

Ab , a 2 , c are in arithmetic progression
Bb , a , c are in geometric progression
Ca , b , c are in geometric progression
Da , b , c are in arithmetic progression

Correct answer

B. b , a , c are in geometric progression

Step-by-step solution

a = 1 + 10 + 10 2 + … … . . + 10 54 = 10 55 - 1 9 b = 10 5 - 1 9 c = 10 5 11 - 1 10 5 - 1 = 10 55 - 1 10 5 - 1 ⇒ a b = c ⇒ a = b c ⇒ b , a , c are in G.P.

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