The 1st term = 1
Explanations:The nth term of an arithmetic sequence is given by the formula:
[tex]T_n=\text{ a + (n-1)d}[/tex]The fourth term will therefore be:
[tex]\begin{gathered} T_4=\text{ a + (4-1)d} \\ T_4=\text{ a + 3d} \end{gathered}[/tex]The fourth term is 3
[tex]\begin{gathered} T_4\text{ = }3 \\ a\text{ + 3d = 3}\ldots\ldots\ldots...\ldots\text{...}(1) \end{gathered}[/tex]The 22nd term will be given by the formula:
[tex]\begin{gathered} T_{22}=\text{ a + (22-1)d} \\ T_{22}\text{ = a + 21d} \end{gathered}[/tex]The 22nd term is 15
[tex]\begin{gathered} T_{22}=\text{ 15} \\ a\text{ + 21d = 15}\ldots\ldots\ldots\ldots.(2) \end{gathered}[/tex]Subtract equation (1) from equation (2)
18d = 12
d = 12/18
d = 2/3
Substitute d = 2/3 into equation (1)
[tex]\begin{gathered} a\text{ + 3(}\frac{2}{3})\text{ = 3} \\ a\text{ + 2 = 3} \\ a\text{ = 3 - 2} \\ a\text{ = 1} \end{gathered}[/tex]Since a represent the 1st term
The first term = 1
