Question

2. Provide the next three terms in the sequence and

state whether the sequence is arithmetic, geometric,
both, or neither.
-243, 81, -27,9

Answer 1

The next three terms of -243, 81, -27, 9 is
`-3,1, (-1)/(3)` The given series is geometric series

Solution:

Given, series is -243, 81, -27, 9, …

We have to find the next three terms of the above given series.

Now, the given series can also be written as

`-243,-243 *\left((-1)/(3)\right)^(1),-243 *\left((-1)/(3)\right)^(2),-243 *\left((-1)/(3)\right)^(3)`

We can say that, above series is in Geometric Progression with first term = -243 and common ratio =
`(-1)/(3)`

Then, next three term would be,

`-243 *\left((-1)/(3)\right)^(4),-243 *\left((-1)/(3)\right)^(5),-243 *\left((-1)/(3)\right)^(6) \rightarrow-3,1, (-1)/(3)`

Hence, the next three terms of given G.P series are
`-3,1, (-1)/(3)`