Question

Which formula can be used to describe the sequence?
Negative two-thirds, −4, −24, −144,...

Answer 1

SOLUTION

TO DETERMINE

The formula to describe the sequence

$\displaystyle \sf{ - \frac{2}{3} \: , \: - 4, - 24, - 144, ....... }$

EVALUATION

Here the given given sequence is

$\displaystyle \sf{ - \frac{2}{3} \: , \: - 4, - 24, - 144, ....... }$

Now

$\displaystyle \sf{ \frac{2nd \: \: term}{1st \: \: term} = \frac{3rd \: \: term}{2nd \: \: term} }$

So the given sequence is Geometric sequence

Here the common ratio

$\displaystyle \sf{ = \frac{ 2nd \: \: term}{1st \: \: term} = \frac{3rd \: \: term}{2nd \: \: term} }$

$= \displaystyle \sf{ \frac{ - 4}{ - \frac{2}{3} } }$

$\displaystyle \sf{ = 4 \times \frac{3}{2} }$

$= 6$

$\sf{Suppose \: nth \: term = a_n \: and \: (n + 1)th \: term = a_{n + 1}}$

Then

$\displaystyle \sf{ \: \: a_{n + 1} = 6 \:a_n \: \: \: where \: \: \: a_1 = - \frac{2}{3} }$

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Learn more from Brainly :-

1. . Find the smallest term of geometric progression 3,5,25/3. that exceeds 100.

https://brainly.in/question/26328002

2. If the non-zero numbers a,b,c are in AP and tan-1a., tan-1b, tan-1c are also in AP, then

(a) a = b = c (b) b²= 2ac

https://brainly.in/question/18766571

Answer 2

SOLUTION

TO DETERMINE

The formula to describe the sequence

EVALUATION

Here the given sequence is

Now

So the given sequence is a geometric sequence

Here the common ratio

Then

━━━━━━━━━━━━━━━━

If you need more help; then you van learn more from Brainly :-

1. . Find the smallest term of geometric progression 3,5,25/3. that exceeds 100.

brainly.in/question/26328002

2. If the non-zero numbers a,b,c are in AP and tan-1a., tan-1b, tan-1c are also in AP, then

(a) a = b = c (b) b²= 2ac

brainly.in/question/18766571