Question

4,8, 21, 59,_,314 what is the _​

Answer 1

Answer:

146

Step-by-step explanation:

 

Pattern:  

4……….8………21………..59……….146…………314

….+4…….+13…….+38………+87………+168

………+32…….+52……..+72………+92

Answer 2

The fifth term of the series is 146.

Given:

A series $4,8,21,59,$ --- $,314$

To find:

The value of the missing term .

Solution:

In the given series, lets assume the missing term is $x$

Now, if we see the difference of the adjacent terms in the series, we get

• $8-4=4$
• $21-8=13$
• $59-21=38$
• $x-59$

• $314-x$

Now, from the derived the values, if we subtract the adjacent terms, we get the values as

1. $a=13-4=9$
2. $b=38-13=25$
3. $c=x-59-38=x-97$
4. $d=314-x-(x-59)$  $=373-2x$

From the first two terms, we can infer that the terms in the series are the square of every alternate natural numbers starting from $3$ .

From this conclusion, we understand that the third term $c$ is square of the number $7$ that is $49.$

Hence,

$x-97=49$

$x=146$

Similarly,

$d=81$

$373-2x=81$

$2x=292$

Hence, $x=146$

Final answer:

Hence, the fifth term of the series is 146.