Respuesta :
The correct answer is:
4.
Explanation:
Taking these numbers as groups of three, we have 2, 7, 8; 3, 12, 9.
In the first group, we can see that we first add 5 and then add 1.
The next group seems to start from the next consecutive number. That is, the first group starts with 2, and the next group starts with 3. The next terms in the second group are found by adding 5 to the second term of the first group (12 = 7+5) and then adding 1 to the third term of the first group (9=8+1); this is because we added 5 and added 1 previously.
Following this pattern, the next group of three would start from the next consecutive number up, 4. The next two terms would be 17 (12+5=17) and 10 (9+1=10).
The next term of teh sequence [tex]2,7,8,3,12,9[/tex] is [tex]\fbox{\begin\\\ 4\\\end{minispace}}[/tex].
Further explanation:
The sequence given in the question is [tex]2,7,8,3,12,9[/tex].
The objective is to obtain the next term of the given sequence.
Group the terms of the given sequence. Consider that two groups are formed such that the terms [tex](2,7,8)[/tex] are placed in group [tex]1[/tex] and the terms [tex](3,12,9)[/tex] are place in group [tex]2[/tex].
[tex]\fbox{\begin\\\ Group 1\rightarrow (2,7,8)\\\end{minispace}}[/tex]
[tex]\fbox{\begin\\\ Group 2\rightarrow (3,12,9)\\\end{minispace}}[/tex]
From the above two groups it is observed that first term of second group is obtained when the first term of group [tex]1[/tex] is increased by [tex]1[/tex] unit.
[tex]\fbox{\begin\\\ 3\rightarrow (2+1)\\\end{minispace}}[/tex]
From group [tex]1[/tex] and group [tex]2[/tex] it is observed that the second term of the group [tex]2[/tex] is obtained when second term of group [tex]1[/tex] is increased by [tex]5[/tex] units.
[tex]\fbox{\begin\\\ 12\rightarrow (7+5)\\\end{minispace}}[/tex]
From group [tex]1[/tex] and group [tex]2[/tex] it is observed that the thirdterm of the group [tex]2[/tex] is obtained when thirdterm of group [tex]1[/tex] is increased by [tex]1[/tex] unit.
[tex]\fbox{\begin\\\ 9\rightarrow (8+1)\\\end{minispace}}[/tex]
Therefore, the relation between the elements of the two groups is given as follows:
[tex]\fbox{\begin\\\ (2\rightarrow3) (7\rightarrow12) (8\rightarrow9)\\\end{minispace}}[/tex]
Now, following the same pattern for the given sequence, the next term of sequence is obtained when the first term of group [tex]2[/tex] is increased by [tex]1[/tex] unit.
[tex]\fbox{\begin\\\ 4\rightarrow (3+1)\\\end{minispace}}[/tex]
This implies that the next term of the given sequence is [tex]4[/tex].
Therefore, the next term of the sequence [tex]2,7,8,3,12,9[/tex] is [tex]\fbox{\begin\\\ 4\\\end{minispace}}[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Sequence
Keywords: Series, sequence, logic, (2,7,8,3,12,9), groups, next term, successive term, mathematics, critical thinking, numbers, addition, subtraction, pattern, rule.
