Question

Find the next term in the alpha-numeric series:
$Z1A,X2D,V6G,T21J,R88M,P445P,?$
A.$N2676S$
B.$N2676T$
C.$T2670N$
D.$T2676N$

Answer 1

Hint: Here, we will first observe the series and find the pattern between the alphabets by which each term is starting and similarly, by which each term is ending. Then we will find the pattern of numbers that are in the middle of the terms. After finding the pattern, we will use the same pattern to find the required next term of the given series.

Complete step-by-step answer:
Given series is: $Z1A,X2D,V6G,T21J,R88M,P445P,?$
Now, first of all, we will observe the pattern of this series.
As we can see, each term of this series is starting with an alphabet
And, then alphabets are going in a decreasing order and there is a difference of 2 between each alphabet:
$Z - 2 = X - 2 = V - 2 = T - 2 = R - 2 = P - 2 = N$
Hence, we can say that the required next term will start from the letter $N$……………………….$\left( 1 \right)$
Now,
The series is consisting of the numbers making a series of:
$1,2,6,21,88,445,?$
Hence, if we try to break the logic of this series then, we can write this series as:
$1,\left( {1 \times 1 + 1} \right),\left( {2 \times 2 + 2} \right),\left( {6 \times 3 + 3} \right),\left( {21 \times 4 + 4} \right),\left( {88 \times 5 + 5} \right),?$
Hence, the next term will be: $445 \times 6 + 6 = 2670 + 6 = 2676$
Therefore, the next term will contain the number 2676………………………………$\left( 2 \right)$
Finally, as we can see, each term of this series is ending with an alphabet.
Alphabets are going in an ascending order and there is an addition of 3 to each preceding alphabet:
$A + 3 = D + 3 = G + 3 = J + 3 = M + 3 = P + 3 = S$
Hence, we can say that the required next term will end with the letter $S$……………………….$\left( 3 \right)$
Hence, from $\left( 1 \right)$, $\left( 2 \right)$ and $\left( 3 \right)$,
Our required next term of the given series $Z1A, X2D, V6G, T21J, R88M, P445P,?$ becomes:
$N2676S$
Therefore, option A is the correct answer.

Note: Alpha-numeric series is that series which consists of a combination of both the alphabets as well as the numbers. In this series, the letters and numbers, in fact sometimes some symbols are combined together in such a way that they form a logical pattern or sequence and by observing their positions and relations with the preceding and the next term, we find the relationship between them. Thus, these types of series are different from the usual series as here; there is a relation between each number as well as each alphabet.