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ICSE Class 10 Answered

Q1) Find 5 geometric means between 1 and 27. Q2) Find the sum of first n terms : 4+44+444+............ Send fast.. ..
Asked by Pradeep | 06 Mar, 2019, 08:17: AM
answered-by-expert Expert Answer
If 5 geometric means are inserted between 1 and 27 , then 27 is the 7th term in Geometric progression
 
if r is the common ratio,  27 = r6   or √3
 
hence the GP is  :   1 , √3 , 3, 3√3, 9, 9√3, 27
 
--------------------------------------------
 
S = 4+44+444.............  = 4(1+11+111........ ) = (4/9) [ 9+99+999.......... ]
 
S = (4/9)[  (10-1)+ (100-1)..........................(10n - 1) ] = (4/9) [ (10+100+1000.............+10n ) - n ]
 
S = (4/9) [ { 10×(10n - 1)/9 } - n ]
Answered by Thiyagarajan K | 06 Mar, 2019, 09:19: AM

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