3rd and 5th term of a G.P are 25 and 100 respectively. Find the 7th term:
___, ___, 25, ___, 100, ___, ?
We could use formulas but the easiest way is
1. Let r = the common ratio,
2. the 4th term has to equal the 3rd term, 25, times r. So fill in the
3rd term as 25r:
___, ___, 25, 25r, 100, ___, ?
3. Then the 5th term has to equal the 4th term, 25r, times r.
4. Get the equation from
×r = 
(25r)r = 100
25r² = 100
r² = 4
r = ±2
Aha! There are two solutions for r, so we will use ±r for both:
5. Get the 6th term by multiplying the 5th term, 100 by ±2 getting ±200
___, ___, 25, 25r, 100, ±200, ?
6. Get the 7th term by multiplying the 6th term, ±200, by ±2, and
regardless of whether r=+2 or r=-2, the 7th term will be +400
___, ___, 25, 25r, 100, ±200, 400
If we like we can get the whole progressions:
One way the progression could be is this:
6.25, 12.5, 25, 50, 100, 200, 400
and the other way is
6.25, -12.5, 25, -50, 100, -200, 400
But either way the 7th term is 400.
Edwin
