Question

Find the pattern and use it to list the nth term in the sequence. 3, 9, 27, 81, 243 ...

Answer 1

The pattern is formed a geometric sequence

The nth term of the sequence is $a_{n}=3^{n}$

Step-by-step explanation:

The formula of the nth term of a geometric sequence is:

$a_{n}=ar^{n-1}$ , where

• a is the first term
• r is the common ratio between the consecutive terms

∵ The pattern is 3 , 9 , 27 , 81 , 243

∵ 9 ÷ 3 = 3

∵ 27 ÷ 9 = 3

∵ 81 ÷ 27 = 3

∵ 243 ÷ 81 = 3

- There is a common ratio 3 between each two consecutive terms

∴ The pattern is formed a geometric sequence

∵ The first term is 3

∴ a = 3

∵ The common ratio is 3

∴ r = 3

- To find the nth term substitute a and r in the formula above

∵ $a_{n}=ar^{n-1}$

∴ $a_{n}=3(3)^{n-1}$

- Remember we add the powers of the same base with multiplication

∵ 3 × $3^{n-1}$ = $3^{1+n-1}$

∴ 3 × $3^{n-1}$ = $3^{n}$

∴ $a_{n}=3^{n}$

∴ The nth term of the sequence is  $a_{n}=3^{n}$

Learn more:

You can learn more about the sequences in brainly.com/question/1522572

#LearnwithBrainly