The first term in a sequence is $x$. Each of the following terms is obtained by doubling the previous term and then adding 4 . If the third term is 52 , then $x$ equals
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

## Part B: Each correct answer is worth 6.
Solution 1

To get from one term to the next, we double and add 4 .

Since the first term is $x$, the second term is $2 x+4$.

Since the second term is $2 x+4$, the third term is $2(2 x+4)+4=4 x+12$.

Since the third term equals 52 , then $4 x+12=52$ so $4 x=40$ or $x=10$.

## Solution 2

To get from one term to the next, we double and add 4.

Therefore, to get from one term to the previous term, we subtract 4 and divide by 2 .

Since the third term is 52 , then subtracting 4 gives 48 and dividing by 2 gives 24 , which is the second term.

Since the second term is 24 , then subtracting 4 gives 20 and dividing by 2 gives 10 , which is the first term.

Thus, $x=10$.

ANSWER: (D)