Question

Find the a5 in a geometric sequence where a1 = −81 and r =
`-(1)/(3)`

Answer 1

We need to use the formula for the nth term of a geometric sequence:

an = a1 * r^(n-1)

where:
an = the nth term
a1 = the first term
r = the common ratio

We are given a1 = -81 and r = √3. To find a5, we substitute n = 5 into the formula:

a5 = a1 * r^(5-1)
a5 = -81 * (√3)^(4)
a5 = -81 * 3
a5 = -243

Therefore, the fifth term in the geometric sequence is -243.