Justify whether it is true to say that the sequence having following nth term is an A.P.$a_n = 2n – 1$

Given:

$a_n = 2n – 1$

To do:

We have to justify whether it is true to say that the sequence defined by $a_n = 2n – 1$ is an A.P. 

Solution:

To  check whether the sequence defined by $a_n = 2n – 1$ is an A.P., we have to check whether the difference between any two consecutive terms is equal.

Let us find the first few terms of the sequence by substituting $n=1, 2, 3....$

When $n=1$,

$a_1=2(1)-1$

$=2-1$

$=1$

$a_2=2(2)-1$

$=4-1$

$=3$

$a_3=2(3)-1$

$=6-1$

$=5$

$a_4=2(4)-1$

$=8-1$

$=7$

Here,

$d=a_2-a_1=3-1=2$

$d=a_3-a_2=5-3=2$

$d=a_4-a_3=7-5=2$

$d=a_2-a_1=a_3-a_2=a_4-a_3$

Hence, the given sequence is an A.P.

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Updated on: 10-Oct-2022

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