Question

find a pattern for the sequence below. use the pattern to find the next three terms. 1, 4, 9, 16, 25, _

Explanation:

Step1: Identify the pattern

The sequence is $1 = 1^2$, $4=2^2$, $9 = 3^2$, $16=4^2$, $25 = 5^2$. The $n$-th term of the sequence is $n^2$.

Step2: Find the 6th term

For $n = 6$, the term is $6^2=36$.

Step3: Find the 7th term

For $n = 7$, the term is $7^2 = 49$.

Step4: Find the 8th term

For $n = 8$, the term is $8^2=64$.

Answer:

36
49
64