Sureeeeee
A.)
1.) Find the 19th term of the sequence for which [tex]a_1=15[/tex] and [tex]d=-3[/tex].
Solution:
[tex]a_n=a_1+(n-1)d[/tex]
[tex]a_{19}=15+(19-1)(-3)[/tex]
[tex]a_{19}=15+(18)(-3)[/tex]
[tex]a_{19}=15-54[/tex]
[tex]a_{19}=39[/tex]
2.) Find the 12th term of the sequence for which [tex]a_1=4[/tex] and [tex]d=\frac{1}{2}[/tex].
Solution:
[tex]a_n=a_1+(n-1)d[/tex]
[tex]a_{12}=4+(12-1)(\frac{1}{2})[/tex]
[tex]a_{12}=4+(11)(\frac{1}{2})[/tex]
[tex]a_{12}=4+\frac{11}{2}[/tex]
[tex]a_{12}=\frac{4}{1} +\frac{11}{2}[/tex]
[tex]a_{12}=\frac{8+11}{2}[/tex]
[tex]a_{12}=\frac{19}{2}[/tex]
B.)
1.) In the arithmetic sequence -4, 0, 4, 8, ... which term equals 116?
Solution:
[tex]a_n=a_1+(n-1)d[/tex]
[tex]116=-4+(n-1)(4)[/tex]
[tex]116=-4+4n-4[/tex]
[tex]116+4+4=+4n[/tex]
[tex]4n=124[/tex]
[tex]\frac{4n}{4} = \frac{124}{4}[/tex]
[tex]n = 31[/tex]st term
2.) In the arithmetic sequence 27, 21, 15, 9, ... which term equals -93?
Solution:
[tex]a_n=a_1+(n-1)d[/tex]
[tex]-93=27+(n-1)(-6)[/tex]
[tex]-93=27-6n+6[/tex]
[tex]-93-27-6=-6n[/tex]
[tex]-6n=-126[/tex]
[tex]\frac{-6n}{-6} =\frac{-126}{-6}[/tex]
[tex]n = 21[/tex]st term
