The next three terms of -243, 81, -27, 9 is [tex]-3,1, \frac{-1}{3}[/tex] 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
[tex]-243,-243 \times\left(\frac{-1}{3}\right)^{1},-243 \times\left(\frac{-1}{3}\right)^{2},-243 \times\left(\frac{-1}{3}\right)^{3}[/tex]
We can say that, above series is in Geometric Progression with first term = -243 and common ratio = [tex]\frac{-1}{3}[/tex]
Then, next three term would be,
[tex]-243 \times\left(\frac{-1}{3}\right)^{4},-243 \times\left(\frac{-1}{3}\right)^{5},-243 \times\left(\frac{-1}{3}\right)^{6} \rightarrow-3,1, \frac{-1}{3}[/tex]
Hence, the next three terms of given G.P series are [tex]-3,1, \frac{-1}{3}[/tex]
