All categories

3 years ago

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

Mathematics

1 answer:

Ede4ka [16]3 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

A veterinarian is going to administer a medication which has a 3.2 liquid to drug

Margaret [11]

The he gives some drugs

4 0

3 years ago

The table shows certain values of a cubic function

Nadusha1986 [10]

Considering the given table, we have that:

The function has a relative maximum when x is near 3.

As x approaches positive infinity, the value of the function approaches negative infinity.

<h3>When a function has a relative maximum?</h3>

A function has a relative maximum when it changes from increasing to decreasing.

Looking at the given table, it happens when x is near 3.

Also, looking at the table, for x > 3 the function is decreasing, hence as x approaches positive infinity, the value of the function approaches negative infinity.

More can be learned about functions at brainly.com/question/24737967

#SPJ1

3 0

2 years ago

Find the 6th term of a geometric sequence with t1=5 and r = -1/2

Hoochie [10]

In this item, we are to calculated for the 6th term of the geometric sequence given the initial value and the common ratio. This can be calculated through the equation,

An = (A₀)(r)ⁿ ⁻ ¹
where An is the nth term, A₀ is the first term (in this item is referred to as t₀), r is the common ratio, and n is the number of terms.

Substitute the known values to the equation,

An = (5)(-1/2)⁶ ⁻ ¹
An = -5/32

Hence, the answer to this item is the third choice, -5/32.

5 0

3 years ago

3x-7y=17 when x=-3,0,3

NeX [460]

$3x-7y=17\\-7y=17-3x\ \ \ \ |:(-7)\\y=-\frac{17}{7}+\frac{3}{7}x\\\\When\ x=-3:\\y=-\frac{17}{7}+\frac{3}{7}\cdot(-3)\\y=-\frac{17}{7}-\frac{9}{7}\\y=-\frac{26}{7}=-3\frac{5}{7}\\\\When\ x=0:\\y=-\frac{17}{7}+\frac{3}{7}\cdot0\\y=-\frac{17}{7}=-2\frac{3}{7}\\\\When\ x=3:\\y=-\frac{17}{7}+\frac{3}{7}\cdot3\\y=-\frac{17}{7}+\frac{9}{7}\\y=-\frac{8}{7}=-1\frac{1}{7}$

4 0

3 years ago

Can someone just answer one n show all the work plz it will help a lot

rosijanka [135]

Step-by-step explanation:

this is the anwser it is inverse trigonometry

8 0

3 years ago