the third and sixth terms of a geometric sequence are -75 and -9375 respectively.Find the first term common ratio and explicit rule for n terms
In a geometric sequence, the terms are,
a0 = a, a1 = ar, a2 = ar^2, a3 = ar^3, ..., an = ar^n
where r is the common ratio.
We have,
3rd term is a2 = ar^2 = -75
6th term is a5 = ar^5 = -9375
ar^5 / ar^2 = (-9375) / (-75) = 125
r^3 = 125
r = 5 => a = -3 (the first term)
The rule is: an = (-3)(75)^n, where an is the n+1 th term