Which term of the AP: \( 53,48,43, \ldots \) is the first negative term?

Given:

Given A.P. is \( 53,48,43, \ldots \)

To do:

We have to find which term of the given A.P. is its first negative term.

Solution:

Here,

$a_1=53, a_2=48, a_3=43$

Common difference $d=a_2-a_1=48-53=-5$

The first negative term of the given A.P. $=53-5\times11=53-55=-2$   ($53-5\times10=3$ is the last positive term)

We know that,

nth term $a_n=a+(n-1)d$

Therefore,

$a_{n}=53+(n-1)(-5)$

$-2=53+n(-5)-1(-5)$

$-2-53=-5n+5$

$55+5=5n$

$5n=60$

$n=\frac{60}{5}$

$n=12$

Hence, the first negative term is the 12th term of the given A.P.  

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Updated on: 10-Oct-2022

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