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For what value of $n$, the nth term of the two AP: $3,\ 8,\ 13,.......$ and $19,\ 22,\ 25,......$ will be equal?
Given: nth term of the two AP: $3,\ 8,\ 13,.......$ and $19,\ 22,\ 25,......$ will be equal.
To do: To find the value of $n$.
Solution:
$A_1 =3,\ 8,\ 13$
$a_{n_{1}}=a+(n−1)d$
$=3+(n−1)5$ $(here\ a=3,\ d=5)$
$=3+5n−5$
$=5n−2$
$A_2=19,\ 22,\ 25$
$a_{n_{2}}=a+(n−1)d$
$=19+(n−1)3$ $(here\ a=19,\ d=3)$
$=19+3n−3$
$=16+3n$
$\because a_{n_{1}}=a_{n_{2}}$ $( As\ per\ question)$
$\Rightarrow 5n−2=16+3n$
$\Rightarrow 5n−3n=16+2$
$\Rightarrow 2n=18$
$\Rightarrow n=9$
Updated on: 10-Oct-2022
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