Question

find the 10th term of the geometric sequence 1/4,-1/2,1,-2 ........

Answer 1

a = 1/4

r = (-1/2)/(1/4) = -2

10th Term = a * r ^ n-1

= (1/4) * (-2)^10 - 1

= (1/4) * (-2)^9

= (1/4) * (-1) * 2^9

= (-1) 2^9-2

= (-1) 2^7

= (-128)

Answer 2

Given:

A geometric sequence

1/4, -1/2, 1, -2 ...

To find:

The 10th term of the geometric sequence.

Solution:

As we know that in a geometric sequence that has a = first term, r = common ratio, the nth term is given by using the formula:

${n}^{th} \: term = a {(r)}^{n - 1}$

Now,

as given, we have

A geometric sequence:

1/4, -1/2, 1, -2 ....

Here,

The first term, a = 1/4

The common ratio, r

$= \frac{ second \: term}{first \: term}$

$= \frac{ - 1}{2} \div \frac{1}{4}$

$= \frac{ - 1}{2} \times 4$

$= - 2$

So,

the 10th term of the geometric sequence

$= \frac{1}{4} {( - 2)}^{10 - 1}$

$= \frac{1}{4} ( { - 2)}^{9}$

$= \frac{ { (- 2)}^{2} \times {( - 2)}^{7} }{4}$

$= {( - 2)}^{7}$

$= - 128$

Hence, the 10th term of the geometric sequence is -128.