36.6k views
1 vote
find the missing terms of the arithmetic sequence 24,?,?,?,68the answer choices are A. 36,45,58 B. 36,48,56 C.35,46,57 D.33,47,55

1 Answer

6 votes

The answer is 35, 46, 57.

To find this result, we can proceed as follows:

1. We have that the general formula for an arithmetic sequence is given by:


a_n=a_1+(n-1)d

Where

• a1 is the first element of the sequence

,

• d is the common difference of the arithmetic sequence

2. We have that the first term is 24, and the fifth term is 68. Then we have:


\begin{gathered} a_5=a_1+(5-1)d \\ a_5=68,a_1=24 \\ 68=24+(4)d \end{gathered}

3. Now, we can find the common difference, d, as follows:


\begin{gathered} 68-24=24-24+4d \\ 44=4d \\ \end{gathered}

4. We can divide both sides of the equation by 4:


\begin{gathered} (44)/(4)=(4)/(4)d \\ 11=d \\ d=11 \end{gathered}

Therefore, the common difference is d = 11.

5. The general formula for this arithmetic sequence is, therefore:


\begin{gathered} a_n=24+(n-1)11 \\ a_n=24+n(11)+(-1)11 \\ a_n=24+11n-11 \\ a_n=24-11+11n \\ a_n=13+11n \end{gathered}

6. Finally, to find the second, the third, and the fourth term, we have:


\begin{gathered} a_2=13+11(2)=13+22\Rightarrow a_2=35 \\ a_3=13+11(3)=13+33\Rightarrow a_3=46 \\ a_4=13+11(4)=13+44\Rightarrow a_4=57 \\ a_5=13+11(5)=13+55\Rightarrow a_5=68 \end{gathered}

Therefore, in summary, we have, then, that the missing terms of the arithmetic sequence are 35, 46, 57 (option C.)

User Toto
by
6.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.