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$d=137-17=120,\frac{⟶}{m15\mathrm{sing}\text{term}},137$d=137-17=120,(longrightarrow)/(m 15 sing " term "),137,
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It seems like there is a typo in the question. However, based on the given information, the common difference is correctly computed as $d=137-17=120$d=137-17=120, where $137$137 is the next term and $17$17 is a previous term.
To find the 15th term in this arithmetic sequence, we need to use the formula:
${a}_{n}={a}_{1}+\left(n-1\right)d$a_(n)=a_(1)+(n-1)d
where ${a}_{n}$a_(n) is the $n$nth term, ${a}_{1}$a_(1) is the first term, $d$d is the common difference, and $n$n is the number of terms.
We can plug in the given information to find the first term ${a}_{1}$a_(1):
$17={a}_{1}+\left(1-1\right)120$17=a_(1)+(1-1)120
Simplifying, we get:
$17={a}_{1}$17=a_(1)
Now, we can use the formula to find the 15th term, where $n=15$n=15:
${a}_{15}=17+\left(15-1\right)120$a_(15)=17+(15-1)120
Simplifying, we get:
${a}_{15}=17+14\left(120\right)$a_(15)=17+14(120)
${a}_{15}=1697$a_(15)=1697
Therefore, the 15th term in this arithmetic sequence is $1697$1697.
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