Question
Write the sequence with $n^{th}$ term:
$a_n = 6 - n.$
Show the all of the above sequences form A.P.
$a_n = 6 - n.$
Show the all of the above sequences form A.P.
✓
Answer
$a_n=6-n$
Now,to show that it is an A.P, we will find its few terms by substituting $n =1,2,3$
So, Substituting $n=1$, we get $a_1=6-1 a_1=5$
Substituting $n=2$, we get $a_2=6-2 a_2=4$
Substituting $n=3$, we get $a_3=6-3 a_3=3$
Further, for the given to sequence to be an A.p.
Common difference $(d)=a_2-a_1=a_3-a_2$
Here, $a_2-a_1=4-5=-1$
Also, $a_3-a_2=3-4=-1$
Since $a_2-a_1=a_3-a_2$
Hence, the given sequence is an A.P.
Now,to show that it is an A.P, we will find its few terms by substituting $n =1,2,3$
So, Substituting $n=1$, we get $a_1=6-1 a_1=5$
Substituting $n=2$, we get $a_2=6-2 a_2=4$
Substituting $n=3$, we get $a_3=6-3 a_3=3$
Further, for the given to sequence to be an A.p.
Common difference $(d)=a_2-a_1=a_3-a_2$
Here, $a_2-a_1=4-5=-1$
Also, $a_3-a_2=3-4=-1$
Since $a_2-a_1=a_3-a_2$
Hence, the given sequence is an A.P.
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