Question

2. Provide the next three terms in the sequence and

Answer 1

The next three terms of -243, 81, -27, 9 is $-3,1, \frac{-1}{3}$ 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

$-243,-243 \times\left(\frac{-1}{3}\right)^{1},-243 \times\left(\frac{-1}{3}\right)^{2},-243 \times\left(\frac{-1}{3}\right)^{3}$

We can say that, above series is in Geometric Progression with first term = -243 and common ratio = $\frac{-1}{3}$

Then, next three term would be,

$-243 \times\left(\frac{-1}{3}\right)^{4},-243 \times\left(\frac{-1}{3}\right)^{5},-243 \times\left(\frac{-1}{3}\right)^{6} \rightarrow-3,1, \frac{-1}{3}$

Hence, the next three terms of given G.P series are $-3,1, \frac{-1}{3}$