Answer :
Certainly! Let's find the first three terms of the sequence given by the function \( T(n) = 5n^2 \).
### Calculating the terms:
1. First term ( \( n = 1 \) ):
[tex]\[ T(1) = 5 \cdot 1^2 = 5 \cdot 1 = 5 \][/tex]
So, the first term is \( 5 \).
2. Second term ( \( n = 2 \) ):
[tex]\[ T(2) = 5 \cdot 2^2 = 5 \cdot 4 = 20 \][/tex]
So, the second term is \( 20 \).
3. Third term ( \( n = 3 \) ):
[tex]\[ T(3) = 5 \cdot 3^2 = 5 \cdot 9 = 45 \][/tex]
So, the third term is \( 45 \).
### Summary:
The first three terms of the sequence are:
[tex]\[ 5, 20, \text{ and } 45 \][/tex]
### Calculating the terms:
1. First term ( \( n = 1 \) ):
[tex]\[ T(1) = 5 \cdot 1^2 = 5 \cdot 1 = 5 \][/tex]
So, the first term is \( 5 \).
2. Second term ( \( n = 2 \) ):
[tex]\[ T(2) = 5 \cdot 2^2 = 5 \cdot 4 = 20 \][/tex]
So, the second term is \( 20 \).
3. Third term ( \( n = 3 \) ):
[tex]\[ T(3) = 5 \cdot 3^2 = 5 \cdot 9 = 45 \][/tex]
So, the third term is \( 45 \).
### Summary:
The first three terms of the sequence are:
[tex]\[ 5, 20, \text{ and } 45 \][/tex]
