Question

1. in a children’s story, double dan the dragonfly is growing fast. his body length is doubling every month. at the beginning of the story, his length is 1 cm. a) create a table to show how dan’s body length increases every month for ten months.

Explanation:

Step1: Analyze the growth pattern

The length doubles each month. So, it follows a geometric sequence where the first term \(a_1 = 1\) and the common ratio \(r = 2\). The formula for the \(n\)th term of a geometric sequence is \(a_n=a_1\times r^{n - 1}\).

Step2: Calculate the length for each month

• Month 1: \(a_1=1\times2^{1 - 1}=1\) cm
• Month 2: \(a_2=1\times2^{2 - 1}=2\) cm
• Month 3: \(a_3=1\times2^{3 - 1}=4\) cm
• Month 4: \(a_4=1\times2^{4 - 1}=8\) cm
• Month 5: \(a_5=1\times2^{5 - 1}=16\) cm
• Month 6: \(a_6=1\times2^{6 - 1}=32\) cm
• Month 7: \(a_7=1\times2^{7 - 1}=64\) cm
• Month 8: \(a_8=1\times2^{8 - 1}=128\) cm
• Month 9: \(a_9=1\times2^{9 - 1}=256\) cm
• Month 10: \(a_{10}=1\times2^{10 - 1}=512\) cm

Answer:

Month	Length (cm)
2	2
3	4
4	8
5	16
6	32
7	64
8	128
9	256
10	512