From the question stem:
The first term is 3
The second term is 3*2 + 2 = 8
The third term is 8*2 + 2 = 18

We can see that when the unit digit 8 is multiplied by 2 it ends with 6 and when 2 is added it becomes 8 hence all the terms except the first have their units digit as 8. In total there are 9 such terms
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Explanation

After the first term in the sequence, every term has a units digit of 8:

\(Q_1 = 3\)
\(Q_2 = 2(3) + 2 = 8\)
\(Q_3 = 2(8) + 2 = 18\)
\(Q_4 = 2(18) + 2 = 38\)
\(Q_5 = 2(38) + 2 = 78\)
…

So 8 is the units digit nine out of the first ten times.
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