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

The ratio of peanuts to total nuts in a bag of mixed nuts is 3 : 7. If the bag has 56 total nuts, how many are peanuts?

DedPeter [7]

Answer:

24 peanuts

Step-by-step explanation:

5 0

1 year ago

Read 2 more answers

What is the value? I'm marking brainliest!!

tensa zangetsu [6.8K]

Answer:

103

Step-by-step explanation:

simplify to 81 + 27 - 5

4 0

2 years ago

Read 2 more answers

Write an equation that has a graph with the shape of y = x^2, but shifted left 3 units.

svetoff [14.1K]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}\\\\
--------------------\\\\$

$\bf % template detailing
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\$

$\bf \bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

now, with that template in mind, let's see

$\bf y=x^2\implies 
\begin{array}{llll}
y=(&1x&-0)^2\\
&B&C
\end{array}$

so, just change C to +3, thus C/B is 3/1

6 0

3 years ago

Which equation has the same solution as 2x^2+16x-10=0

dmitriy555 [2]

D
Divide the whole thing by 2
2(X^2+8x-5)
X^2+8x. =5
Half of 8 is 4 sq it so you add 16
X^2+8x+16= 5+16
(X+4)^2=21

8 0

3 years ago

Read 2 more answers

Find the solutions of the quadratic equation -9c² +2 +3 = 0.

Tresset [83]

Given that,

An equation : -9c² +2c +3 = 0

To find,

Find the value of x.

Solution,

We have, -9c² +2c +3 = 0

We can solve it using the formula as follows :

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here, a = -9, b = 2 and c =3

Put the values,

$c=\dfrac{-2\pm \sqrt{(2)^2-4(-9)(3)}}{2(-9)}\\\\c=\dfrac{-2+\sqrt{(2)^{2}-4(-9)(3)}}{2(-9)}, \dfrac{-2-\sqrt{(2)^{2}-4(-9)(3)}}{2(-9)}\\\\c=-0.47, 0.69$

So, the solution are -0.47 and 0.69.

8 0

3 years ago