Find the next term in the sequence: [tex]\( \frac{D}{5}, \frac{G}{9}, \frac{J}{14}, \frac{M}{20}, ? \)[/tex]
Options:
(A) [tex]\( \frac{Q}{26} \)[/tex]
(B) [tex]\( \frac{O}{26} \)[/tex]
(C) [tex]\( \frac{Q}{27} \)[/tex]
(D) [tex]\( \frac{P}{27} \)[/tex]
Answer (1)
To find the next term in the sequence 5 D , 9 G , 14 J , 20 M , ? , we need to analyze patterns in both the numerators (letters) and the denominators (numbers).
Numerators (Letters):
The sequence of letters is D, G, J, M.
These letters are increasing by three positions in the alphabet:
D is the 4th letter,
G is the 7th letter,
J is the 10th letter,
M is the 13th letter.
To find the next letter, continue this pattern of adding 3 to the position in the alphabet:
M is the 13th letter, so add 3: 13 + 3 = 16.
The 16th letter is P.
Denominators (Numbers):
The sequence of denominators is 5, 9, 14, 20.
Let's look at the differences between consecutive terms:
9 - 5 = 4
14 - 9 = 5
20 - 14 = 6
The differences are increasing by 1 each time (4, 5, 6).
To find the next number, add 7 to 20: 20 + 7 = 27.
Therefore, the next term in the sequence is 27 P .
Hence, the correct answer is option (D) 27 P .
