The 2nd term in a geometric sequence is -4 and the 5th term is 32
a + ar + a r^2 + a r^3 + a r^4
ar = -4
a r^4 = 32
a = -4/r
(-4/r) r^4 = 32
r^3 = -8
so r = -2
and a = 2
To find the common ratio in a geometric sequence, you can use the formula:
common ratio = (n-th term) / (previous term),
In this case, we are given that the 2nd term is -4 and the 5th term is 32.
To find the common ratio, we can use the following steps:
Step 1: Calculate the difference between the 5th term and the 2nd term.
difference = 32 - (-4) = 36.
Step 2: Calculate the difference between the 2nd term and the 1st term (which we don't know yet).
Since we know the 2nd term (-4), we can use the common ratio formula: -4 = (1st term) / (common ratio).
Step 3: Rearrange the formula to solve for the 1st term:
1st term = -4 * common ratio.
Step 4: Substitute the 1st term into the common ratio formula as (-4 * common ratio) to get:
-4 = (-4 * common ratio) / common ratio.
Step 5: Simplify the equation:
-4 = -4.
Since both sides of the equation are equal, we can conclude that the common ratio is 1.
Therefore, in this geometric sequence, the common ratio is 1.