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ANEK [815]
3 years ago
11

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

Mathematics
1 answer:
Mazyrski [523]3 years ago
5 0
<h3><u>Answer:</u></h3>

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

<h3><u>Step-by-step explanation:</u></h3>

A sequence is given to us is , and we need to find expression for nth term of the sequence. The given sequence is ,

\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 .

<u>And nth term of an Harmonic Progression is </u><u>:</u><u>-</u>

\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}}}

<h3><u>Hence</u><u> </u><u>the</u><u> </u><u>nth</u><u> </u><u>term</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>given</u><u> </u><u>sequ</u><u>ence</u><u> is</u><u> given</u><u> by</u><u> </u><u>¹</u><u>/</u><u>n</u><u> </u><u>.</u><u> </u></h3>
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