geoff planted dahlias in his garden. In the first year, geoffs garden produced 4 bulbs. In the second year it producted 8 bulbs, and in the third year it produced 16 bulbs. How many bulbs will Geoff have in the 10th year?
A: 2,048
B: 1,024
C: 40
D: 32
1 answer
This is a geometric sequence with first term $4$ and common ratio $2$, since each year the number of bulbs doubles. Therefore, the $n$th term of the sequence is $4 \cdot 2^{n-1}$. So in the 10th year, we have $4 \cdot 2^{10-1} = 4 \cdot 2^9 = 2^{11} = \boxed{\textbf{(A) } 2,048}$.
2 answers