Question

The 11th term in a geometric sequence is 48 and the common ratio is −0.8. The 12th term is _________ and the 10th term is ________.

Answer 1

Answer:

The 12th term is -38.4 and the 10th term is -60.

Step-by-step explanation:

Consider the geometric sequence,

$S=\{a,\ ar,\ ar^{2},\ ar^{3},\ ...\}$

The first term is, a.

The common ratio is, r.

The formula to compute the common ratio is:

$r=\frac{T_{n}}{T_{n-1}}$

The information provided is:

T₁₁ = 48

r = -0.8

Compute the 12th term as follows:

    $r=\frac{T_{n}}{T_{n-1}}$

$-0.8=\frac{T_{12}}{T_{11}}\\\\0.8=\frac{T_{12}}{48}\\\\T_{12}=48\times-0.8\\\\T_{12}=-38.4$

The 12th term of the geometric sequence is -38.4.

Compute the 10th term as follows:

    $r=\frac{T_{n}}{T_{n-1}}$

$-0.8=\frac{T_{11}}{T_{10}}\\\\0.8=\frac{48}{T_{10}}\\\\T_{10}=\frac{48}{-0.8}\\\\T_{10}=-60$

The 10th term of the geometric sequence is -60.