Write the sequence with nth term:$a_n=5+2n$Show that all of the above sequences form A.P.

Given:

$a_n=5+2n$

To do:

We have to write the sequence and show that it forms an A.P.

Solution:

To find the given sequence we have to substitute $n=1, 2, 3.....$ in $a_n=5+2n$.

Therefore,

$a_1=5+2(1)$

$=5+2$

$=7$

$a_2=5+2(2)$

$=5+4$

$=9$

$a_3=5+2(3)$

$=5+6$

$=11$

$a_4=5+2(4)$

$=5+8$

$=13$

The sequence formed is $7, 9, 11, 13,.....$.

For the given sequence to form an A.P., the difference between any two consecutive terms should be equal.

Here,

$d=a_2-a_1=9-7=2$

$d=a_3-a_2=11-9=2$

$d=a_4-a_3=13-11=2$

This implies,

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

Hence, the given sequence forms an A.P. 

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Updated on: 10-Oct-2022

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