All categories

2 years ago

Find the explicit formula for the sequence? -1,4,-16,64......

Mathematics

1 answer:

Ede4ka [16]2 years ago

5 0

The explicit formula for given sequence is: $a_n = -1 . (-4)^{n-1}$

Step-by-step explanation:

Given sequence is:

-1,4,-16,64.....

We can see that there is no same difference between consecutive terms so we will find common ratio to see if it is a geometric sequence.

Here

$a_1 = -1\\a_2 = 4\\a_3 = -16\\a_4 = 64\\r = \frac{a_2}{a_1} = \frac{4}{-1} = -4\\r = \frac{a_3}{a_2} = \frac{-16}{4} = -4$

The explicit formula for geometric sequence is:

$a_n = a_1r^{n-1}$

Putting the values of r and a1

$a_n = -1 . (-4)^{n-1}$

Hence

The explicit formula for given sequence is: $a_n = -1 . (-4)^{n-1}$

Keywords: Geometric sequence, common ratio

Learn more about geometric sequence at:

#learnwithBrainly

You might be interested in

How many different 4 digit even numbers can be written using 0,5,6,3,8,7?

kherson [118]

Step-by-step explanation:

I assume the digits cannot be repeated in the numbers.

and that we don't want any numbers that start with 0, as that would be considered a 3- digit number, right ?

so, under these assumptions we have the question of in how many ways can we pull 4 digits out of 6.

if the sequence of the pulled digits would not matter, it would be combinations C(6, 4).

but because we are building actual numbers, the sequence does matter, and we use permutations P(6, 4).

P(6, 4) = 6!/(6-4)! = 6!/2! = 6×5×4×3 = 360

so, we can create 360 different numbers.

but not all of them are wanted.

we don't want the ones that start with 0. how many are those ?

since we are handling all digits in the same way and priority, there are an equal amount of numbers that start with a 0, or a 5, or a 6, or a 3, or a 8, or a 7.

so, 1/6 of the 360 numbers start with a 0, and we need to subtract them :

360 - 60 = 300 really 4-digit numbers

and from these 300 we only want even numbers. that means they can only end with 0, 6 or 8.

in the same way as for the first position, we have 1/6 of the more 300 numbers that end with one of these digits.

we allow 3 digits, so we have

3×1/6 × 300 = 1/2 × 300 = 150

that means we can write 150 different 4-digit even numbers out of these 6 digits.

6 0

1 year ago

Luna has $50 when she got to the carnival. After riding 12 rides she had $26 left. what was the price of each ride? Which equati

marusya05 [52]

2 dollars a ride, since 50-26 is 24 and 24/12 is 2

4 0

2 years ago

Read 2 more answers

Sketch a model to show how to combine the following fractions: 4/3 + 2/3 =

DerKrebs [107]

4/3 + 2/3= (4+2)/3= 6/3= 2

3 0

2 years ago

Read 2 more answers

A ramp 24 ft long rises to a platform that is 20 ft off the ground. find x , the angle of elevation of the ramp. round your answ

lara31 [8.8K]

$sin(x)= \frac{BC}{AC}= \frac{20}{24} \approx 0.8333 \ \ \to \ \ x\approx56.4^o$

3 0

2 years ago

A circle with circumference \blue{6}6start color #6495ed, 6, end color #6495ed has an arc with a 60^\circ60

Bingel [31]

Answer:

$\Delta s = 1$

Step-by-step explanation:

The length of the arc is directly proportional to the angle of the arc, whose measure is determined by simple rule of three:

$\Delta s = \left(\frac{60^{\circ}}{360^{\circ}} \right)\cdot (6)$

$\Delta s = 1$

8 0

2 years ago

Read 2 more answers