Find whether 55 is a term of the AP: $ 7,10,13,-\cdots $ or not. If yes, find which term it is.
Given:
Given AP is \( 7,10,13,-\cdots \)
To do:
We have to find whether 55 is a term of the given AP and which term it is if it is a term of the given AP.
Solution:
Let $a$ be the first term, $d$ the common difference and $a_n=55$ be the $n$th term.
This implies,
$a_1=a=7$
$d=a_2-a_1$
$=10-7=3$
$a_{n}=a+(n-1)d$
$55=7+(n-1)3$
$55-7=3n-3$
$48+3=3n$
$3n=51$
$n=17$
Here, $n$ is a positive integer.
Therefore, $55$ is a term of the given AP.
Hence, 55 is 17th term of the given AP.
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