babeeb0oL

2021-08-17

Find the 55th term of the arithmetic sequence 2, -18, -38,

tabuordy

Formula to find the nth term of an arithmetic sequence is
${a}_{n}={a}_{1}+d\left(n-1\right)$
${a}_{2}-{a}_{1}=-18-2=-20$
${a}_{3}-{a}_{2}=-38-\left(-18\right)=-38+18=-20$

Common difference $=d=-20$
${a}_{n}={a}_{1}+d\left(n-1\right)$
${a}_{55}=2+\left(-20\right)\left(55-1\right)$
${a}_{55}=2+\left(-20\right)\left(54\right)$
${a}_{55}=2-1080$
${a}_{55}=-1078$
The 55th term of an arithmetic sequence is -1078.

Jeffrey Jordon

Answer is given below (on video)

To find the 55th term of an arithmetic sequence, we can use the formula:
${a}_{n}={a}_{1}+\left(n-1\right)d$ where ${a}_{n}$ is the $n$th term, ${a}_{1}$ is the first term, $n$ is the term number, and $d$ is the common difference.
In this case, the first term, ${a}_{1}$, is 2, and the common difference, $d$, can be found by subtracting the second term from the first term:
$d={a}_{2}-{a}_{1}=\left(-18\right)-2=-20$
Substituting the values into the formula, we have:
${a}_{55}=2+\left(55-1\right)\left(-20\right)$
Now, let's calculate the 55th term:
${a}_{55}=2+\left(54\right)\left(-20\right)=2-1080=-1078$
Therefore, the 55th term of the arithmetic sequence 2, -18, -38 is $-1078$.

Nick Camelot

$-1078$
Explanation:
Given:
${a}_{n}={a}_{1}+\left(n-1\right)d,$
where ${a}_{n}$ is the nth term, ${a}_{1}$ is the first term, $n$ is the position of the term we want to find, and $d$ is the common difference between consecutive terms.
In this case, the first term ${a}_{1}$ is 2, and the common difference $d$ can be found by subtracting the second term from the first term:
$d=-18-2=-20.$
Now we can substitute the values into the formula to find the 55th term:
${a}_{55}=2+\left(55-1\right)\left(-20\right).$
Simplifying the expression inside the parentheses:
${a}_{55}=2+54\left(-20\right).$
Multiplying:
${a}_{55}=2-1080.$
Finally, performing the subtraction:
${a}_{55}=-1078.$
Therefore, the 55th term of the arithmetic sequence $2,-18,-38$ is $-1078$.

Do you have a similar question?