Let, the geometric sequence is such that, value of common ratio is less than 1.
The Sequence is
[tex]6^{n-1},6^{n-2},6^{n-3},.....,.......\infinity.[/tex]
The Geometric Squence is infinite geometric sequence, as there are uncountable terms in the sequence.
⇒So, From [tex]6^{n-1}[/tex], to infinity, there will be n terms which will be integers when , n≥1.
⇒Put, n=1,
Number of terms which are Positive Integers =1 which is [tex]6^{n-1}[/tex].
⇒When, n=2
Number of terms which are Positive Integers =2 which is [tex]6^{n-1},6^{n-2}[/tex].
⇒When, n=3
Number of terms which are Positive Integers =3, which is [tex]6^{n-1},6^{n-2},6^{n-3}[/tex].
..........
So,⇒ when , n=r
Number of terms which are Positive Integers =r, which is [tex]6^{n-1},6^{n-2},6^{n-3},6^{n-4},........6^{n-r}[/tex].
