2 months ago

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

Mathematics

1 answer:

lawyer [12.5K]2 months ago

8 0

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

Step-by-step explanation:

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

a represents the first term of the sequence
r signifies the common ratio between any two consecutive terms
$r=\frac{a_{2}}{a_{1}}$ = $\frac{a_{3}}{a_{2}}$

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

∵ The first term is $\frac{-2}{3}$

∵ The second term is -4

∴ $\frac{-4}{\frac{-2}{3}}=6$

∵ The third term is -24

∴ $\frac{-24}{-4}=6$

∵ The fourth 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 consistent ratio between two consecutive terms

∴ The sequence qualifies as a geometric sequence

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

∵ a = $\frac{-2}{3}$

∵ r = 6

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

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

Learn more:

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