Question

Complete the series:
\[Z{A_5},{Y_4}B,X{C_6},{W_3}D,\_\_\_\_\_\_\_\]
a) \[{E_7}V\]
b) \[{V_2}E\]
c) \[V{E_5}\]
d) \[V{E_7}\]

Answer 1

Hint: We need to observe the series very carefully and follow the pattern. We need to look for three series here. We observe that First Letters are in Alphabetical order but also in reverse order. The second letter is in alphabetical order that begins with \[A\]. Now the numbers in subscript need to be observed. We see that they are allocated alternatively first with the second alphabet and then with the first alphabet. Also, we need to observe that the numbers with the second letter follow forward counting starting from \[5\] and the number with the first alphabet follow backward counting starting from \[4\]. We see that the last given term has a subscript number with the first alphabet and so the next term will have its subscript number with the second alphabet.

Complete step-by-step solution:
Observing the first letter of each term, we have
First letter of first term is \[Z\]
First letter of second term is \[Y\]
First letter of third term is \[X\]
First letter of fourth term is \[W\]
We see that they are in reverse alphabetical order.
So, First letter of the next term i.e. Fifth term will be \[V - - - - - - - (1)\]
Now, Observing the second letter of each term,
Second letter of first term is \[A\]
Second letter of second term is \[B\]
Second letter of third term is \[C\]
Second letter of fourth term is \[D\]
We see that the second letter of each term is in alphabetical order.
So, Second letter of the next term i.e. Fifth term will be \[E - - - - - - (2)\]
Now, observing the pattern of subscript numbers.
We see that the terms at odd places have their subscript number with the second alphabet and the terms at even places have their subscript number with the first number. We need to find the Fifth term i.e. an odd term. So, we will have the subscript number with the second alphabet.
Now, the subscript numbers at odd places follow forward counting starting from \[5\]and the subscript numbers at even places follow backward counting starting from \[4\]. Since we have to find the Fifth term i.e. an odd term we will focus on the pattern that odd terms follow. As the subscript number at odd places follow forward counting starting from \[5\], we have
Subscript number at first place is \[5\]
Subscript number at third place is \[6\]
So, the subscript number at fifth place will be \[7 - - - - - - (3)\]
Now, this number is to be allocated with the second term as we have seen above.
Hence, Combining (1), (2) and (3), we see
The Fifth term will be \[V{E_7}\].
Therefore, the correct option is (d).

Note: The pattern we are following needs to be observed very carefully because these patterns are usually very tricky and missing out even a small thing will lead to wrong answer. The series can follow another series within like we saw for the subscript numbers. So, that needs to be taken care of. We must notice the similarities and differences between the terms.