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Bunuel
In a certain sequence of numbers, each term after the first term is found by multiplying the preceding term by 2 and then subtracting 3 from the product. If the 4th term in the sequence is 19, which of the following numbers are in the sequence?

I. 11
II. 22
III. 35

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

a1=x
a2= 2x-3
a3=4x-9 =
a4=8x-21=19; x=5
so a5= 38-3; 35
a4=11
IMO D; possible
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Given: In a certain sequence of numbers, each term after the first term is found by multiplying the preceding term by 2 and then subtracting 3 from the product.
Asked: If the 4th term in the sequence is 19, which of the following numbers are in the sequence?

T_1 = x
T_2 = 2x -3
T_3 = 2(2x -3) - 3 = 4x - 9
T_4 = 2(4x-9) -3 = 8x - 21 = 19
x = 5

Sequence = {5, 7, 11, 19, 35,...}

I. 11 - in the sequence
II. 22 - not in the sequence
III. 35 - in the sequence


IMO D
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