Question

Which formula can be used to describe the sequence? -2/3,-4,-24,-144...

Answer 1

The formula can be used to describe the sequence is $a_{n}=\frac{-2}{3}(6)^{n-1}$

Step-by-step explanation:

The formula of the nth term of the geometric sequence is $a_{n}=a(r)^{n-1}$ , where

• a is the first term of the sequence
• r is the common ratio between each two consecutive terms
• $r=\frac{a_{2}}{a_{1}}$ = $\frac{a_{3}}{a_{2}}$

∵ The sequence is $\frac{-2}{3}$ , -4 , -24 , -144 , .......

∵ The 1st term is $\frac{-2}{3}$

∵ The 2nd term is -4

∴ $\frac{-4}{\frac{-2}{3}}=6$

∵ The 3rd term is -24

∴ $\frac{-24}{-4}=6$

∵ The 4th term is -144

∴ $\frac{-144}{-24}=6$

∵  $\frac{a_{2}}{a_{1}}$ = $\frac{a_{3}}{a_{2}}$ =  $\frac{a_{4}}{a_{3}}$ = 6

∴ There is a constant ratio between each two consecutive terms

∴ The sequence is a geometric sequence

∵ The formula of the nth term of the geometric sequence is $a_{n}=a(r)^{n-1}$

∵ a = $\frac{-2}{3}$

∵ r = 6

∴ The formula of the sequence is $a_{n}=\frac{-2}{3}(6)^{n-1}$

The formula can be used to describe the sequence is $a_{n}=\frac{-2}{3}(6)^{n-1}$

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You can learn more about sequences in brainly.com/question/7221312

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