Question

The final number in the series V, VIII, XII, XVII, _ is XX.
A.Yes
B.No

Answer 1

Hint: Here the series contains roman numerals. First we will convert them into a decimal number system for our convenience. This can be solved by observing the pattern and relating the terms of the series according to the pattern.

Complete step-by-step answer:
Roman numerals are number systems that originated in ancient Rome. Numbers in this system are represented by combinations of letters from the Latin alphabet.
The 7 different letters which denote some specific numbers are,

Letters	I	V	X	L	C	D	M
Numbers	1	5	10	50	100	500	1000

We can use these seven letters to represent the numbers in a very concise manner, for this problem let us see the first 10 roman numerals,

Numbers	1	2	3	4	5	6	7	8	9	10
Roman Numerals	I	II	III	IV	V	VI	VII	VII	XI	X

XII can be written as X+II= $ $ 10 + 2 = 12 $ $ similarly
XVII = X+VII= $ 10 + 7 = 17 $
XX=X+X= $ $ 10 + 10 = 20 $ $
Therefore the given series in decimal number system is $ $ 5,8,12,17,\_ $ $
The first term in the series is 5 adding3 to it gives the second term 8 then adding 4 to second term gives the third term 12 and the pattern continues in this manner…. i.e.
 $ \eqalign{
  & 5 + 3 = 8 \cr
  & 8 + 4 = 12 \cr
  & 12 + 5 = 17 \cr
  & 17 + 6 = 23 \cr} $
Therefore the term after $ 17 $ is $ 23 $ .
Hence the given option that the term after $ 17 $ is $ 20 $ is wrong.
Hence the correct option is NO.
So, the correct answer is “Option B”.

Note: While solving questions like this where we have to find the next term of the series, the important step is the identification of patterns in the series which has to be done properly. We have to observe carefully how the successive terms of the series are related to each other to identify the pattern. If the difference between successive terms is constant then we can use Arithmetic progression to find the missing term.