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O GRAPHING=Finding the next terms of an arithmetic sequence with integersThe first three terms of an arithmetic sequence are as follows.+1, 2, 5Find the next two terms of this sequence.1, 2,5. 0 00 05x

O GRAPHING=Finding the next terms of an arithmetic sequence with integersThe first-example-1
User Nhrobin
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1 Answer

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\begin{gathered} \text{fourth term}\rightarrow8 \\ \text{fifth term}\rightarrow11 \end{gathered}

Step-by-step explanation

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term,it is give by the expression:


a_n=a_1+(n-1)d

so

Step 1

use the given data to find the arithmetic sequence

so

let


\begin{gathered} a_1=-1 \\ a_2=2 \\ a_3=5 \end{gathered}

so

a) find the common difference


\begin{gathered} \text{Difference}_1=a_2-a_1=2-(-1)=2+1=3 \\ \text{Difference}_1=5-2=3 \\ \end{gathered}

hence the common difference is 3


d=\text{ 3}

now, chec the first term and replace in the formula


\begin{gathered} \text{first term}\rightarrow-1 \\ \text{difference}\rightarrow3 \\ \text{replace} \\ a_n=a_1+(n-1) \\ a_n=-1+(n-1)3 \end{gathered}

Step 2

now, use the expression to find teh netx two terms

a)


\begin{gathered} a_n=-1+(n-1)3 \\ \text{for n= 4,replace} \\ a_4=-1+(4-1)3 \\ a_4=-1+(3)3=-1+9=8 \\ a_4=8 \end{gathered}

b) fifth term


\begin{gathered} a_n=-1+(n-1)3 \\ \text{for n= 4,replace} \\ a_5=-1+(5-1)3 \\ a_5=-1+(4)3=-1+12=11 \\ a_5=11 \end{gathered}

so, the answer is


8,11

I hope this helps you

User Tony Davis
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