# 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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