Question

A laboratory is making a new formula for a deadly virus. The formula follows a certain pattern. One of the important elements is missing from the series. Choose the correct option for the missing element.
$A_2{E}_7{I}_{23}$ , $D_3{H}_{10}{L}_{32}$ , ? , $J_5{N}_{16}{R}_{50}$

• A. $G_4{K}_{13}{O}_{41}$
• B. $G_4{K}_{13}{P}_{42}$
• C. $G_4{K}_{13}{O}_{42}$
• D. $G_4{K}_{13}{P}_{41}$

Answer 1

The correct option is A $G_4{K}_{13}{O}_{41}$

Let's identify the pattern in the formula.
The first letter of the formula follows a pattern of +3.
$A\left(1\right)\stackrel{(+3)}{\to }D\left(4\right)\stackrel{(+3)}{\to }G\left(7\right)\stackrel{(+3)}{\to }J\left(10\right)$
The first letter of the missing element is J.

Similarly, the other letters also follow the same pattern.
$E\left(5\right)\stackrel{(+3)}{\to }H\left(8\right)\stackrel{(+3)}{\to }K\left(11\right)\stackrel{(+3)}{\to }N\left(14\right)$
The second letter of the missing element is K.

And for the third letter:
$I\left(9\right)\stackrel{(+3)}{\to }L\left(12\right)\stackrel{(+3)}{\to }O\left(15\right)\stackrel{(+3)}{\to }R\left(18\right)$
The third letter of the missing element is O.

Now, let's identify the numbers in the subscript.
The numbers follow the pattern: $(\times 3+1)$, $(\times 3+2)$
$2\times 3+1=7$
$7\times 3+2=23$

The next number is starting from 3.
$3\times 3+1=10$
$10\times 3+2=32$

The next number should start from 4.
$4\times 3+1=13$
$13\times 3+2=41$

Hence, this is the number series the missing formula follows.
Let's see the last one.

The next number should start from 5.
5 × 3 + 1 = 16
16 × 3 + 2 = 50

Hence, the missing element is $G_4{K}_{13}{O}_{41}$.