Timed the first term of a geometric sequence is –2 and the common ratio is -1/4. what are the next three terms of the sequence?

Hello from MrBillDoesMath!

 The second bullet point from the top (  +1/2, -1/8, + 1/32)

Discussion:

Let's write out the geometric sequence

First term of sequence

-2                                

Second term of sequence

-2 * (-1/4)   = + 1/2         -- multiply by the ratio to the first power

Third  term of sequence

-2 * ( (-1/4) ^2)  = (-2) * (1/16)  = - 1/8   -- multiply by square of ratio

Fourth term in series

-2 * (( (-1/4)^3) = -2 * ( - 1/64) = + 1/32     -- multiply by cube of ratio

Regards, MrB

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: