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lozanna [386]
3 years ago
11

Find the three arithmetic means in this sequence. 14, __, __, __, 26

Mathematics
2 answers:
Alina [70]3 years ago
6 0
26 - 14 = 12
12 ÷ 4 = 3

26 - 3 = 23
23 - 3 = 20
20 - 3 = 17

14, 17, 20, 23, 26

Answer: The three missing arithmetic means in this sequence are 17, 20, 23.



Verizon [17]3 years ago
3 0

Answer:

14, 17, 20, 23, 26

Step-by-step explanation:

Add by three's

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Step-by-step explanation:

<h3>Question-1:</h3>

by order pair we obtain:

\displaystyle  \begin{cases}   \displaystyle 3p = 2p - 1 \dots \dots i\\2q - p =  1 \dots  \dots ii\end{cases}

cancel 2p from the i equation to get a certain value of p:

\displaystyle  \begin{cases}   \displaystyle p =  - 1 \\2q - p =  1 \end{cases}

now substitute the value of p to the second equation:

\displaystyle  \begin{cases}   \displaystyle p =  - 1 \\2q - ( - 1) =  1 \end{cases}

simplify parentheses:

\displaystyle  \begin{cases}   \displaystyle p =  - 1 \\2q  +  1=  1 \end{cases}

cancel 1 from both sides:

\displaystyle  \begin{cases}   \displaystyle p =  - 1 \\2q  =  0\end{cases}

divide both sides by 2:

\displaystyle  \begin{cases}   \displaystyle p =  - 1 \\q  =  0\end{cases}

<h3>question-2:</h3>

by order pair we obtain:

\displaystyle  \begin{cases}   \displaystyle 2x - y= 3 \dots \dots i\\3y= x + y \dots  \dots ii\end{cases}

cancel out y from the second equation:

\displaystyle  \begin{cases}   \displaystyle 2x - y= 3 \dots \dots i\\ x = 2y \dots  \dots ii\end{cases}

substitute the value of x to the first equation:

\displaystyle  \begin{cases}   \displaystyle 2.2y-y= 3 \\ x = 2y \end{cases}

simplify:

\displaystyle  \begin{cases}   \displaystyle 3y= 3 \\ x = 2y \end{cases}

divide both sides by 3:

\displaystyle  \begin{cases}   \displaystyle y= 1 \\ x = 2y \end{cases}

substitute the value of y to the second equation which yields:

\displaystyle  \begin{cases}   \displaystyle y= 1 \\ x = 2 \end{cases}

<h3>Question-3:</h3>

by order pair we obtain;

\displaystyle  \begin{cases}   \displaystyle  2p  + q = 2 \dots \dots i\\3q  + 2p =  3 \dots  \dots ii\end{cases}

rearrange:

\displaystyle  \begin{cases}   \displaystyle  2p  + q = 2 \\2p  +  3q=  3 \end{cases}

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\displaystyle  \begin{array}{ccc}   \displaystyle  2p  + q = 2 \\2p  +  3q=  3 \\  \hline   - 2q  =  - 1 \\  q =  \dfrac{1}{2} \end{array}

substitute the value of q to the first equation:

\displaystyle 2.p+  \frac{1}{2}  = 2

make q the subject of the equation:

\displaystyle p =   \frac{3}{4}

hence,

\displaystyle  q =  \frac{1}{2} \\ p =   \frac{3}{4}

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