# convert Sn=(6+66+666....Nth term) into GP and find Nth term

Aman Bansal
592 Points
9 years ago

Dear Rohan,

The given sequence is 8, 88, 888, 8888…
This sequence is not a G.P. However, it can be changed to G.P. by writing the terms as
Sn = 8 + 88 + 888 + 8888 + …………….. to n terms

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Thanks

Aman Bansal

shubham tibra
15 Points
9 years ago

Sn =6/9(9+99+999....n)     sn= 6/9(10+100+1000...n -1-1-1-1.....n) sn =6/9(gp with a=10 and r=10 upto nterm - summation of 1 i.e. n) solving it u will get the answer

anshumanpandey
13 Points
5 years ago
By anshuman pandey AIS With arpit and ankit pandey
Its too easy (6+66+666+6666+.............n terms)

take common 6 ( 1+11+111............)  multiply by 9
then 6/9 (9+99+999+.........)
6/9(10+100+1000+......-1-1-1-1 n)
Helper
13 Points
4 years ago
6+66+666+..6(1+11+111+...)Multiply&Divide by 96/9(9+99+999+.....)6/9[(10-1)+(100-1)+(1000-1)+...]6/9[10+10²+10³+....]-[(1)(1)...... n times]Here a=10 and r=10 Hence, S = a.r^n-1/ r-1S= 10(10^n-1)/10-1S=10(10^n-1)/9=> 6/9[10/9(10^n-1) - n]