Sure, let's find the sum of the squares of the first 10 positive integers.
The sequence you provided is the set of squares of the first 10 positive integers. That is:
[tex]\[ 1 = 1^2 \][/tex]
[tex]\[ 4 = 2^2 \][/tex]
[tex]\[ 9 = 3^2 \][/tex]
[tex]\[ 16 = 4^2 \][/tex]
[tex]\[ 25 = 5^2 \][/tex]
[tex]\[ 36 = 6^2 \][/tex]
[tex]\[ 49 = 7^2 \][/tex]
[tex]\[ 64 = 8^2 \][/tex]
[tex]\[ 81 = 9^2 \][/tex]
[tex]\[ 100 = 10^2 \][/tex]
To find the sum of these squares, we sum each of these terms:
[tex]\[ 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 \][/tex]
The sum of these terms is:
[tex]\[ 1 + 4 = 5 \][/tex]
[tex]\[ 5 + 9 = 14 \][/tex]
[tex]\[ 14 + 16 = 30 \][/tex]
[tex]\[ 30 + 25 = 55 \][/tex]
[tex]\[ 55 + 36 = 91 \][/tex]
[tex]\[ 91 + 49 = 140 \][/tex]
[tex]\[ 140 + 64 = 204 \][/tex]
[tex]\[ 204 + 81 = 285 \][/tex]
[tex]\[ 285 + 100 = 385 \][/tex]
So, the sum of the squares of the first 10 positive integers is:
[tex]\[ 385 \][/tex]
Therefore, the final answer is [tex]\( 385 \)[/tex].
The question and these steps take us through calculating the sum of squares for the first 10 integers, leading us to the result [tex]\( 385 \)[/tex].
