Question

Find the indicated term of the given geometric sequence. a1 = 14, r = –2, n = 11

Answer 1

Answer:

$a_{11} = 14336$

Step-by-step explanation:

The general formula for the twelfth term of a geometric sequence is:

$a_n = a_1(r)^{n-1}$

Where $a_1$ is the first term and r is the common ratio

In this case we know that:

$a_1 = 14\\r=-2$

The equation is:

$a_n = 14(-2)^{n-1}$

So for $n = 11$ we look for $a_{11}$

$a_{11} = 14(-2)^{11-1}$

$a_{11} = 14(-2)^{10}$

$a_{11} = 14336$

Answer 2

Answer:

$11^{th}$ term = 14336

Step-by-step explanation:

We are given the first term $a _ 1 = 1 4$ and  common ratio $r = - 2$ of a geometric sequence and we are to find the $11^{th}$ term of this sequence.

We know that the formula to find the $n^{th}$ term in a geometric sequence is given by:

$n^{th}$ term = $a r ^ { n - 1 }$

Substituting the given values in the above formula:

$11^{th}$ term = $14 \times(-2)^{11-1}$

$11^{th}$ term = $14 \times(-2)^{10}$

$11^{th}$ term = 14336