Write the sequence with nth term:$a_n=6-n$Show that all of the above sequences form A.P.
Given:
$a_n=6-n$
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 $a_n=6-n$.
Therefore,
$a_1=6-1$
$=5$
$a_2=6-2$
$=4$
$a_3=6-3$
$=3$
$a_4=6-4$
$=2$
The sequence formed is $5, 4, 3, 2,.....$.
For the given sequence to form an A.P., the difference between any two consecutive terms should be equal.
Here,
$d=a_2-a_1=4-5=-1$
$d=a_3-a_2=3-4=-1$
$d=a_4-a_3=2-3=-1$
This implies,
$a_2-a_1=a_3-a_2=a_4-a_3=d$
Hence, the given sequence forms an A.P.
Related Articles
- Write the sequence with nth term:$a_n=3+4n$Show that all of the above sequences form A.P.
- Write the sequence with nth term:$a_n=5+2n$Show that all of the above sequences form A.P.
- Write the sequence with nth term:$a_n=9-5n$Show that all of the above sequences form A.P.
- Justify whether it is true to say that the sequence having following nth term is an A.P.$a_n = 1 + n + n^2$
- Justify whether it is true to say that the sequence having following nth term is an A.P.$a_n = 2n – 1$
- Show that the sequence defined by $a_n = 3n^2 – 5$ is not an A.P.
- Justify whether it is true to say that the sequence having following nth term is an A.P.$a_n = 3n^2 + 5$
- Show that the sequence defined by $a_n = 5n – 7$ is an A.P., find its common difference.
- If the nth term of the A.P. $9, 7, 5, …$ is same as the nth term of the A.P. $15, 12, 9, …$ find $n$.
- Find the sum of first 20 terms of the sequence whose nth term is $a_n = An + B$.
- Find the sum of the first 15 terms of each of the following sequences having nth term as$x_n = 6 - n$
- Find the sum of the first 15 terms of each of the following sequences having nth term as$a_n = 3 + 4n$
- The sum of first n terms of an A.P. is $5n – n^2$. Find the nth term of this A.P.
- Consider the sequence 3, 6, 9, 12, 15, ..(1) Write down the next two terms of the sequence.(ii) Find, in terms of n, a formula for the nth term of the sequence.(iii) Hence, find the 105th term.
- Write the first five terms of each of the following sequences whose nth terms are: \( a_{n}=\frac{2 n-3}{6} \)
Kickstart Your Career
Get certified by completing the course
Get Started