naivlingr

2021-08-20

Find the 52nd term of the arithmetic sequence -24,-7, 10

Mayme

1st term, ${a}_{1}=-24$
Common difference, $d=\left(-7\right)-\left(-24\right)=17$
52nd term, ${a}_{52}=a+\left(52-1\right)d=-24+51×17=843$ (answer)

Jeffrey Jordon

Answer is given below (on video)

nick1337

To find the 52nd term of the arithmetic sequence $-24,-7,10$, we can use the formula for the general term of an arithmetic sequence:
${a}_{n}={a}_{1}+\left(n-1\right)d$
where ${a}_{n}$ represents the $n$th term, ${a}_{1}$ is the first term, $n$ is the position of the term, and $d$ is the common difference between consecutive terms.
In this case, ${a}_{1}=-24$ and the common difference is $d=-7-\left(-24\right)=17$.
Substituting these values into the formula, we can find the 52nd term:
${a}_{52}=-24+\left(52-1\right)×17$
Calculating this expression, we have:
${a}_{52}=-24+51×17$
Simplifying further:
${a}_{52}=-24+867$
Thus, the 52nd term of the arithmetic sequence $-24,-7,10$ is $843$.

Don Sumner

843
Explanation:
${A}_{n}={A}_{1}+\left(n-1\right)d$
Where:
${A}_{n}$ is the nth term,
${A}_{1}$ is the first term,
$n$ is the position of the term,
and $d$ is the common difference.
In this case, the first term ${A}_{1}$ is -24, and the common difference $d$ can be determined by subtracting the first term from the second term:
$d=\left(-7\right)-\left(-24\right)$
$d=17$
Now we can substitute the values into the formula to find the 52nd term:
${A}_{52}=-24+\left(52-1\right)·17$
Simplifying the equation:
${A}_{52}=-24+51·17$
Calculating the product:
${A}_{52}=-24+867$
${A}_{52}=843$
Therefore, the 52nd term of the arithmetic sequence -24, -7, 10 is 843.

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