SOLUTION: If the first term of a sequence is 6, the second is 30 and the fourth is 78, what is the fifth term? A) 30 B) 84 C) 102 D) 108 E) 114

Question 1201718: If the first term of a sequence is 6,
the second is 30 and the fourth is 78,
what is the fifth term?
A) 30
B) 84
C) 102
D) 108
E) 114
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
If the first term of a sequence is 6,
the second is 30 and the fourth is 78,
what is the fifth term?
A) 30
B) 84
C) 102
D) 108
E) 114
~~~~~~~~~~~~~~~~~~

It DEPENDS.

It heavily DEPENDS.

It depends on which sequence it is.

--------------------

comment from student: It is linear sequence because the three slope are equal.
The answer is (C) 102. an=24n-18=6(4n-3) a5=[30(5-1)-6(5-2)]/[2-1]=120-18=102

My response. Your comment is INCORRECT, if to consider it as a Math statement.

From the given information, we can not conclude that the 5-th term is in linear sequence with the others term.

We only can assume it, or believe in it, because it is true for other terms.

But in Math, we can not base our proofs or out inferences on our believes; otherwise, it is just not Math.

Also, my Math education is from Math department of one of the best Universities,
so I do not need to have explanations from outside for simple elementary questions.

I do not like, when people come to the forum with questions, and then start explain me that 2x2 is 5 in response to my answer.

. . . - because they believe in it . . .

Your problem is of the class "Guess next number in a sequence without having any info about this number".

        All problems/puzzles/questions of this kind relate to one category,
        which in Math and in English is described by one word " GIBBERISH ".

And I ask you NEVER post this kind of "problems" to this forum in the future.

                Do not litter the Internet.   Keep the Internet clean.

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