harleystanley69
Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

What are the next two terms of the following sequence? -2, 4, -8, 16, ...

Sagot :

devishri1977

Answer:

-32 , 64

Step-by-step explanation:

Geometric sequence

This is a geometric sequaence and each term is obtatained by multiplying the previous number with the common ratio 'r'

          [tex]\sf \boxed{r = \dfrac{second \ term }{first \ term}}[/tex]

[tex]\sf r =\dfrac{4}{(-2)}[/tex]

r = -2

The next two terms ,

   Fifth term = 16 *(-2) = -32

  Sixth term  = (-32) * (-2) = 64

                - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

           What are the next two terms of the following sequence?

[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]

The next two terms are -32 and 64.

[tex]\blue{\textsf{\textbf{\underline{\underline{How to Solve:-}}}}[/tex]

                First of all, let's identify what kind of sequence this is.

The two main types of sequences are:

  • [tex]\textsf{Arithmetic.}[/tex] This is where we add/subtract the same number to get to the following term.
  • [tex]\textsf{Geometric.}[/tex] This is where we multiply/divide by the same number to get to the next term.

In the given sequence, we use multiplication, so we're dealing with a [tex]\textit{geometric sequence}[/tex].

In order to get to the next term, we multiply by -2.

So in order to find the next two terms of the sequence, we take the previous term and multiply it by -2 as follows:

16•(-2)=-32

We've found the 5th term of the geometic sequence.

Now let's find the 6th:

-32•(-2)=64 (the product of a negative and a negative results in a positive)

Summary of Final Answer:-

The next two terms in the sequence are -32 and 64.

Good luck.

                - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.