**Problem : **
What is the common ratio
*r*
in the geometric sequence
.5, 1.5, 4.5, 13.5, 40.5,…
?

**Problem : **
Define the geometric sequence
*a*
_{n} = 2×3^{(}
*n* - 1)
recursively.

**Problem : **
Define the geometric sequence
*a*
_{1} = 4
;
*a*
_{n+1} =
*a*
_{n}
explicitly.

**Problem : **
What is
53×2^{(}
*n* - 1)
?

**Problem : **
What is the limit of the infinite series
2 + 1 + + + ^{ ... }
?