Answer:
The first term is a = 0.4.
Step-by-step explanation:
We are given the indicated terms of an arithmetic sequence; [tex]a_3[/tex] = 1, [tex]a_3_3[/tex] = 22.
As we know that the nth term of the A.P. is given by;
[tex]a_n=a+(n-1)d[/tex]
where, a = first term and d = common difference
Now, the third term of AP is given as 1, this means;
[tex]a_3=a+(3-1)d[/tex]
[tex]a+2d=1[/tex]
a = 1 - 2d --------------- [equation 1}
Also, the 33rd term of AP is given as 22, this means;
[tex]a_3_3=a+(33-1)d[/tex]
[tex]a+32d=22[/tex]
[tex]1-2d+32d=22[/tex] {using equation 1}
[tex]30d=21[/tex]
[tex]d=\frac{21}{30}[/tex]
d = 0.7
Putting the value of d in equation 1 we get;
[tex]a=1-(2 \times 0.7)[/tex]
a = 1 - 1.4 = -0.4
Hence, the first term of an AP is -0.4.
