[tex]\begin{gathered} T_5=\text{ }19 \\ T_6=\text{ }23 \end{gathered}[/tex]
Explanation:
The series: 3 + 7 + 11 + 15 + 19 + 23 + 27 + .....
The formula relating the term to the series :
[tex]T_n=S_{n_{}}-S_{n-1}[/tex]
a) We are to find term 5
To get T5, we will substitute n for 5 in the formula above:
[tex]\begin{gathered} T_5=S_5-S_{5-1} \\ T_5=S_5-S_4 \\ S_5\text{ = 3 + 7 + 11 + 15 + 19 = 55} \\ S_4\text{ = 3 + 7 + 11 + 15 = 36} \end{gathered}[/tex][tex]\begin{gathered} T_5=S_5-S_4\text{ } \\ T_5=\text{ 55 - 36} \\ T_5=\text{ 19} \end{gathered}[/tex]
b) We are to find term 6
To get T6, we will substitute n for 6 in the formula above:
[tex]\begin{gathered} T_6=\text{ }S_6-S_{6-1}\text{ } \\ T_6=\text{ }S_6-S_5\text{ } \\ S_6\text{ = 3 + 7 + 11 + 15 + 19 + 23 = 78} \\ S_5\text{ = 55} \end{gathered}[/tex][tex]\begin{gathered} T_6=\text{ }S_6-S_5\text{ } \\ T_6=\text{ }78\text{ - 55} \\ T_6=\text{ }23 \end{gathered}[/tex]
