missing where? Is it possible that you meant, "What is the next term of the geom. seq. 3/4, 1/2, 1/3, ..... "?
First term, a(1), is 3/4. How do we get 1/2 from 3/4? Divide:
1
-----
2 1 4
------- = ----- * ------ = 4/6, or 2/3. Check this out: r=common factor= 2/3.
3 2 3
----
4
Do we get 1/3 when we multiply 1/2 by 2/3? YES.
Written formally, a(3) = (3/4)(2/3)^(3-1) = (3/4)(2/3)^2 = (3/4)(4/9) = 1/3
What's the next term (the missing term)?
a(4) = (3/4)(2/3)^(4-1) = 2/9 (answer)