Question

Find the 7th term 18,6,2…

Answer 1

If we look at the series, one third of the current term gives the numerical value of the next term.

If we need to express it algebraically, we can write the following equation.

• $a_{n+1}=\frac{a_{n}}{3}$

Therefore, our common multiplier can be found as follows. Because this sequence is a geometric sequence.

• $\frac{a_{n+1}}{a_{n}} =r=\frac{1}{3}$

In geometric sequences, any term can be written in terms of the first term. Below is an example.

• $a_{n}=a_{1}.r^{n-1}$

Since we know the numerical values of the first term and the common factor of the series, we can easily find the seventh term.

• $a_{7}=a_{1}.r^{7-1}$
• $a_{7}=18.(\frac{1}{3} )^6$
• $a_{7}=\frac{2}{81}$