Answer:
[tex]\boxed{\pink{\tt\longmapsto The \ nth \ term \ of \ the \ sequence\ is \ given \ by \ frac{1}{n}}}[/tex]
Step-by-step explanation:
A sequence is given to us is , and we need to find expression for nth term of the sequence. The given sequence is ,
[tex]\bf 1 , \dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5},\dfrac{1}{6}[/tex]
When we flip the numbers , we can clearly see that the number are in Harmonic Progression.
That is when we flip the numbers they are found to be in Arithmetic Progression .
And nth term of an Harmonic Progression is :-
[tex]\boxed{\purple{\bf T_{(Harmonic \ Progression)} = \dfrac{1}{a+(n-1)d}}}[/tex]
Hence here
- Common difference = 1
- First term = 1 .
Substituting the respective values,
[tex]\bf\implies T_{n}= \dfrac{1}{a+(n-1)d} \\\\\bf\implies T_{n} = \dfrac{1}{1+(n-1)1}\\\\\bf\implies T_n = \dfrac{1}{1+n-1}\\\\\bf\implies\boxed{\red{\bf T_{n}=\dfrac{1}{n}}}[/tex]
Hence the nth term of the given sequence is given by ¹/n .
