Question

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

Answer 1

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.)