Question

Question 26 What will be the value of X in the arithmetical number series given below 3/8, 3/16, 3/32, X, 3/64, 3/80 O 1/16 0 5/32 O 1/64 o 1/32​

Answer 1

Step-by-step explanation:

see the answer and write

Answer 2

A. The value of X is $\frac{1}{16}$.

Given,

$\frac{3}{16} ,\frac{3}{32},X ,\frac{3}{64} ,\frac{3}{80}$

To find,

value of X

Concept used,

As, we can see the reciprocal of all the terms differs by 16 means reciprocal of all terms form Arithmetic Progression AP this is in Harmonic Progression, H.P.

Lets reciprocal and find the 4th term in the series.

Reciprocal = $\frac{16}{3} ,\frac{32}{3},\frac{1}{X},\frac{64}{3} ,\frac{80}{3}$

a = $\frac{16}{3}$

d = $\frac{16}{3}$

General formula to find

$a_{n} = a + (n-1)d\\ \\a_{3} = \frac{16}{3} + (2)\frac{16}{3}$

$a_{3} = \frac{48}{3} = \frac{16}{1}$

Therefore, the 4th term in the series is reciprocal of $\frac{16}{1}$ and which is $\frac{1}{16}$.