Math Snap

STEP 1

Assumptions1. The sequence is $\{a_{n}\}$ with known values $a_{0}, a_{1}, a_{}, a_{3}, a_{4}$ which are16,25,36,49,64 respectively.
. The sequence follows a certain pattern which we need to determine.

STEP 2

We observe the given sequence to identify a pattern.$$a_{0} =16, a_{1} =25, a_{2} =36, a_{} =49, a_{4} =64$$

STEP 3

We notice that each number in the sequence is a perfect square.$$a_{0} =^2, a_{1} =5^2, a_{2} =6^2, a_{3} =7^2, a_{} =8^2$$

STEP 4

We can see that the base of the square for each term in the sequence is increasing by1 for each subsequent term.$$a_{n} = (n+4)^2$$

STEP 5

We can now use this pattern to calculate the next four terms in the sequence.$$a_{5} = (5+4)^2, a_{} = (+4)^2, a_{7} = (7+4)^2, a_{8} = (8+4)^2$$

Calculate the values of $a_{5}, a_{6}, a_{}, a_{8}$.
$$a_{5} =9^2 =81, a_{6} =10^2 =100, a_{} =11^2 =121, a_{8} =12^2 =144$$The next four values of the sequence $\{a_{n}\}$ are81,100,121,144.