Question

30 POINTS! Find an explicit formula for the geometric sequence −1,−7,−49,−343 d(n)=

Answer 1

Answer:

$d(n) = { - 7}^{n - 1}$

Step-by-step explanation:

Since the sequence above is a geometric sequence

For an nth term in a geometric sequence

$d(n) = a ({r})^{n - 1}$

where

a is the first term

r is the common ratio

n is the nth term

To find the common ratio divide the previous term by the next term

That's

$r = \frac{ - 7}{ - 1} = 7 \: \: \: \: or \\ r = \frac{ - 49}{ - 7} = 7 \: \: \: or \\ r = \frac{ - 343}{ - 49} = 7$

So the common ratio / r = 7

the first term is - 1

Substitute the values into the above formula

$d(n) = - 1( {7})^{n - 1}$

We have the final answer as

$d(n) = { - 7}^{n - 1}$

Hope this helps you