Question

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

Answer 1

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

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 = ( - 7)/( - 1) = 7 \: \: \: \: or \\ r = ( - 49)/( - 7) = 7 \: \: \: or \\ r = ( - 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