Which term of the AP

Question:

Which term of the AP $9,14,19,24,29, \ldots$ is $379 ?$

Solution:

To Find: we need to find n when an = 379

Given: The series is $9,14,19,24,29, \ldots$ and $a_{n}=379$

$a_{1}=9, a_{2}=14$ and $d=14-9=5$

(Where $a=a_{1}$ is first term, $a_{2}$ is second term, $a_{n}$ is nth term and $d$ is common difference of given $\mathrm{AP}$ )

Formula Used: $a_{n}=a+(n-1) d$

$a_{n}=379=a_{1}+(n-1) 5$

$379-9=(n-1) 5$ [subtract 9 on both side]

$370=(n-1 \diamond \diamond \diamond) 5$

$74=(n-1)$ [Divide both side by 5 ]

$n=75^{\text {th }}$

The $75^{\text {th }}$ term of this AP is equal to 379 .

 

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