Question

Analyze the given sequence
for it's rule and identify the
thirtieth (30th) term 2, 4/3,1,
4/5, 2/3?​

Answer 1

Answer:

not know friend sorry....

Answer 2

Answer:

The correct answer will be -

the 30th term of the sequence is 4/31

$a_{30} = \frac{4}{31}$

Step-by-step explanation:

Step - 1

Given sequence is

$2,\frac{4}{3} , 1,\frac{5}{4} ,\frac{2}{3} ...$

This sequence is an HP (harmonic progression).

$\frac{3}{4} - \frac{1}{2} = \frac{1}{4} \\\\\frac{1}{1} -\frac{3}{4} =\frac{1}{4} \\\\\frac{5}{4} -\frac{1}{1} =\frac{1}{4} \\\\\frac{3}{2} -\frac{5}{4} =\frac{1}{4}$

We can clearly see if we reciprocal the terms, they will form an Arithmetic progression with a common difference d = 1/4

Step - 2

Now the question is to find the 30th term of the given sequence. Taking the reciprocal of the term since the reciprocal of the terms form an AP (Arithmetic Progression).

$\frac{1}{a_{30}} = \frac{1}{2} +(30-1)\times\frac{1}{4} \\\\\frac{1}{a_{30}} = \frac{1}{2} +\frac{29}{4} \\\\\frac{1}{a_{30}} =\frac{2+29}{4} \\\\\frac{1}{a_{30}} =\frac{31}{4} \\\\a_{30} = \frac{4}{31}$

So, the 30th term of the given sequence will be 4/31.

#SPJ3