Question

Find an expression for the nth term (t_n) in each of the following​

Answer 1

Answer:

$\boxed{\pink{\tt\longmapsto The \ nth \ term \ of \ the \ sequence\ is \ given \ by \frac{1}{n}}}$

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 ,

$\boxed{\boxed{\blue{\qquad\bf 1 , \dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5},\dfrac{1}{6}}}}$

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 :-

$\boxed{\purple{\bf T_{(Harmonic \ Progression)} = \dfrac{1}{a+(n-1)d}}}$

Hence here

• Common difference = 1
• First term = 1 .

Substituting the respective values,

$\bf\implies T_{n}= \dfrac{1}{a+(n-1)d} \\\\\bf\implies T_{n} = \dfrac{1}{1+(n-1)1}\\\\\bf\implies T_n = \dfrac{1}{1+n-1}\\\\\bf\implies\boxed{\red{\bf T_{n}=\dfrac{1}{n}}}$

Hence the nth term of the given sequence is given by ¹/n .