ETS Official Quantitative Reasoning Practice Questions, Chapter 7, Practice Set 1, Question 19

I quickly came up with the formula: 2x - 3 = current term (where x = preceding term):

So 2x - 3 = 19
2x = 22
x = 11 --> C

2x - 3 = 11
2x = 14
x = 7

2x - 3 = 7
2x = 10
x =5 --> A

The next term in the sequence would be --> 2x - 3 = 2(19) - 3 = 35 --> F

Therefore, the answer is A, C, F

c

We can easily deduce here the general term of the sequence
\(a_{n+1}\) = \(2 * {a_n}\) - 3

We rewrite the formula for the forth and third term:
\(a_4\) = \(2 * {a_3}\) - 3

We resolve the equation for \(a_3\).
\(a_3\) = \(\frac{(a_4 +3)}{2} = \frac{22}{2}=11\)

Similarly, we calculate the preceding terms:
\(a_3\) = \(2 * {a_2} - 3\)
\(a_2\) = \(\frac{(a_3 +3)}{2} =\frac{14}{2}=7\)(not in the answer choices)

\(a_2\) = \(2 * {a_1}- 3\)
\(a_1\) = \(\frac{({a_2} +3)}{2} = \frac{10}{2}=5\) (in the answer choices)

From here we notice that the terms are smaller and smaller.
The smallest term in the answer choices is 5, so we have to look at higher terms (higher than the one given, which is the \(a_4\))

\(a_5\) =\(2 * {a_4} - 3\)
\(a_5\) =\(2*19 -3 = 35\)

Since we know that the fourth term is 19 and the fifth term is 35 there is no term in between, hence all the answers are:11, 5 and 35

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