Question

Consider the sequence 3, -9, 27, -81, .. Find the 14th term of the sequence.

The 14th term of the sequence is...

Answer 1

-4782969

Explanation:

The pattern can be seen as just multiplying the current number by -3 and repeating for each succeeding number. By that logic, we can just conventionally keep multiplying -3 until we reach the 14th term. In this case, we get the order

`3, -9, 27, -81, 243, -729, 2187, -6561, 19683, -59049, 177147, -531441, 1594323,` and lastly
`-4782969` which is our 14th term.

We can also realize that the 14th term can be found as the 14th power of -3, which also results in
`-4782969`.

Answer 2

let 'a' be the first term, 'd' be the common difference between all the terms of the sequence

Explanation:

therefore, a = 3,

and, d = -9 -3

= -12

hence the 14th term would be,

=> a + 13d

=> 3 + 13( -12 )

=> 3 - 156

=> - 153