avissidep

2021-08-16

Find the 97th term of the arithmetic sequence 17, 26, 35,

firmablogF

Step 1
The given arithmetic sequence is 17,26,35,.......
The first term of A.P. is 17.
The common difference is $26-17=35-26=9$.
Here, $a=17$ and $d=9$
Step 2
The nth term of an A.P. is calculated by ${a}_{n}=a+\left(n-1\right)d$.
Substitute the value of $a=17,d=9$ and $n=97\in {a}_{n}=a+\left(n-1\right)d$.
${a}_{n}=17+\left(97-1\right)9$
$=17+96\cdot 9$
$=17+864$
$=881$
Therefore, the 97th term of the arithmetic sequence is 881.

Jeffrey Jordon

Answer is given below (on video)

alenahelenash

Explanation:
An arithmetic sequence is a sequence in which the difference between consecutive terms is constant. In this case, the common difference is obtained by subtracting the first term from the second term. So, in the given sequence, the common difference ($d$) is:

The formula for the nth term of an arithmetic sequence is:
${a}_{n}={a}_{1}+\left(n-1\right)d,$ where ${a}_{n}$ represents the nth term, ${a}_{1}$ is the first term, $n$ is the term number, and $d$ is the common difference.
Now, substituting the given values into the formula, we have:
${a}_{97}=17+\left(97-1\right)·9.$
Simplifying further:
${a}_{97}=17+96·9.$
Evaluating the expression:
${a}_{97}=17+864.$
Finally, we can compute the value:
${a}_{97}=881.$
Therefore, the 97th term of the arithmetic sequence 17, 26, 35 is 881.

star233

To find the 97th term of an arithmetic sequence, we can use the formula:
${a}_{n}={a}_{1}+\left(n-1\right)d$
where ${a}_{n}$ represents the $n$th term, ${a}_{1}$ is the first term, $n$ is the term number, and $d$ is the common difference.
In this case, the first term ${a}_{1}$ is 17, and the common difference $d$ can be found by subtracting the first term from the second term:
$d=26-17=9$
Now we can substitute the values into the formula to find the 97th term:
${a}_{97}=17+\left(97-1\right)·9$
Calculating this expression, we get:
${a}_{97}=17+96·9=17+864=881$
Therefore, the 97th term of the arithmetic sequence 17, 26, 35 is 881.

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