Show that the sequence defined by $a_n = 5n – 7$ is an A.P., find its common difference.

Given:

$a_n = 5n – 7$

To do:

We have to show that the sequence defined by $a_n = 5n – 7$ is an A.P. and find its common difference.

Solution:

To  show that the sequence defined by $a_n = 5n – 7$ is an A.P., we have to show that 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 $n=1$,

$a_1=5(1)-7$

$=5-7$

$=-2$

$a_2=5(2)-7$

$=10-7$

$=3$

$a_3=5(3)-7$

$=15-7$

$=8$

$a_4=5(4)-7$

$=20-7$

$=13$

Here,

$d=a_2-a_1=3-(-2)=3+2=5$

$d=a_3-a_2=8-3=5$

$d=a_4-a_3=13-8=5$

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

Hence, the given sequence is an A.P. and the common difference is $5$.

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Updated on: 10-Oct-2022

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