The second term of an exponential sequence is 35 and the fourth term is 875. Find the first term
and the common ratio.
Let the first term of the exponential sequence be a and the common ratio be r.
Therefore, the second term is ar and the fourth term is ar^3.
Given that the second term is 35 and the fourth term is 875, we can set up two equations:
ar = 35
ar^3 = 875
From the first equation, we get:
a = 35/r
Substitute this into the second equation:
(35/r)*r^3 = 875
35r^2 = 875
r^2 = 25
r = 5 or -5
If r = 5:
a = 35/5 = 7
If r = -5:
a = 35/-5 = -7
Therefore, the first term of the sequence can be either 7 or -7, and the common ratio can be either 5 or -5.