Certainly! We are given an arithmetic sequence with a specific rule for generating the terms:
[tex]\[ T(n+1) = T(n) + 4 \][/tex]
with the initial term:
[tex]\[ T(1) = 5 \][/tex]
Let's find the first five terms step-by-step:
1. First term:
[tex]\[ T(1) = 5 \][/tex]
2. Second term:
To get the second term [tex]\( T(2) \)[/tex], we add the common difference (4) to the first term:
[tex]\[ T(2) = T(1) + 4 = 5 + 4 = 9 \][/tex]
3. Third term:
To get the third term [tex]\( T(3) \)[/tex], we add the common difference (4) to the second term:
[tex]\[ T(3) = T(2) + 4 = 9 + 4 = 13 \][/tex]
4. Fourth term:
To get the fourth term [tex]\( T(4) \)[/tex], we add the common difference (4) to the third term:
[tex]\[ T(4) = T(3) + 4 = 13 + 4 = 17 \][/tex]
5. Fifth term:
To get the fifth term [tex]\( T(5) \)[/tex], we add the common difference (4) to the fourth term:
[tex]\[ T(5) = T(4) + 4 = 17 + 4 = 21 \][/tex]
Thus, the first five terms of the sequence are:
[tex]\[ 5, 9, 13, 17, 21 \][/tex]
