In sequence \(Q,\) the first number is 3, and each subsequent number in the sequence is determined by doubling the

[M7MBA]

In sequence \(Q,\) the first number is 3, and each subsequent number in the sequence is determined by doubling the previous number and then adding 2. How many times does the digit 8 appear in the units digit of the first 10 terms of the sequence?

A. 9
B. 8
C. 7
D. 6
E. 5

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT

[Scott@TargetTestPrep]

In sequence \(Q,\) the first number is 3, and each subsequent number in the sequence is determined by doubling the previous number and then adding 2. How many times does the digit 8 appear in the units digit of the first 10 terms of the sequence?

A. 9
B. 8
C. 7
D. 6
E. 5

[spoiler]OA=A[/spoiler]

Solution:

The first few terms of the sequence are the following:

3

3 x 2 + 2 = 8

8 x 2 + 2 = 18

18 x 2 + 2 = 38

38 x 2 + 2 = 78

As we can see, the units digit of every term in this sequence after the first term is 8. This is because the units digit of each subsequent term is obtained by multiplying the units digit of the previous term (which is 8) by 2 and adding 2. So, of the first 10 terms, there are 9 terms with a units digit of 8.

Answer: A