Question

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

Answer 1

`11^(th)` term = 14336

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 *(-2)^(11-1)`

`11^(th)` term =
`14 *(-2)^(10)`

`11^(th)` term = 14336

Answer 2

`a_(11) = 14336`

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`