IIT JEE , AIEEE Forum - Mathematics , Algebra

Greatdreams

It is given in the problem that all terms are

100

Now let us take the numbers ......

2,3,4,5,6,7,8,9,10......
So the terms of a G.P are n,2n,4n for common ratio = 2

similarly for others we have
n,3n,9n ; n,4n,16n ; n,5n,25n ....for common ratios respectively 3,4,5......

as it is said that the number cant be > 100,

for n =2...... 4n

100
thus no of terms = 25

for common ratio = 3
no of terms = 11

for common ratio = 4
no of terms = 6

for common ratio = 5
no of terms = 4

in these way

so no of geometric progressions = 25 + 11+ 6+4+2+2+1+1 = 53

edited.......

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