Answer:
The 12th term is -38.4 and the 10th term is -60.
Step-by-step explanation:
Consider the geometric sequence,
[tex]S=\{a,\ ar,\ ar^{2},\ ar^{3},\ ...\}[/tex]
The first term is, a.
The common ratio is, r.
The formula to compute the common ratio is:
[tex]r=\frac{T_{n}}{T_{n-1}}[/tex]
The information provided is:
T₁₁ = 48
r = -0.8
Compute the 12th term as follows:
[tex]r=\frac{T_{n}}{T_{n-1}}[/tex]
[tex]-0.8=\frac{T_{12}}{T_{11}}\\\\0.8=\frac{T_{12}}{48}\\\\T_{12}=48\times-0.8\\\\T_{12}=-38.4[/tex]
The 12th term of the geometric sequence is -38.4.
Compute the 10th term as follows:
[tex]r=\frac{T_{n}}{T_{n-1}}[/tex]
[tex]-0.8=\frac{T_{11}}{T_{10}}\\\\0.8=\frac{48}{T_{10}}\\\\T_{10}=\frac{48}{-0.8}\\\\T_{10}=-60[/tex]
The 10th term of the geometric sequence is -60.
