Question

What is the next two term of the arithmetic sequence 1/81,1/27,1/9

Answer 1

Answer:

1/1

Step-by-step explanation:

1/81=3×3×3×3

1/27=3×3×3

1/9=3×3

1/1=3

Answer 2

Given:

Arithmetic sequence$\[ = \frac{1}{{81}},\frac{1}{{27}},\frac{1}{9},....\]$.

To find: the next two terms in the given arithmetic sequence.

Solution:

Observe the pattern given below formed by expanding each term.

$\[\begin{array}{l}\frac{1}{{81}} = \frac{1}{{3 \times 3 \times 3 \times 3}} \times 3\\\frac{1}{{27}} = \frac{1}{{3 \times 3 \times 3}} \times 3\\\frac{1}{9} = \frac{1}{{3 \times 3}} \times 3\end{array}\]$

Understand that, in each of the term 3 is multiplied which then gives the next the term in the sequence.

Therefore, the next two terms can be

$\[\frac{1}{{81}} \Rightarrow \frac{1}{{3 \times 3 \times 3 \times 3}} \times 3 = \frac{1}{{27}}\]$

$\[\frac{1}{{27}} \Rightarrow \frac{1}{{3 \times 3 \times 3}} \times 3 = \frac{1}{9}\]$

$\[\frac{1}{9} \Rightarrow \frac{1}{{3 \times 3}} \times 3 = \left[ {\frac{1}{3}} \right]\]$

$\[\frac{1}{3} \Rightarrow \frac{1}{3} \times 3 = \left[ 1 \right]\]$

Hence, the next two terms in the given arithmatic sequence are $\[\frac{1}{3}\]$ and $1$ respectively.