Answer:
[tex]S_ {12} = 192[/tex]
Step-by-step explanation:
The nth term of the given arithmetic sequence is
[tex]U_n = 3 + 2n[/tex]
The first term of this series is:
[tex]U_1 = 3 + 2(1) = 5[/tex]
The last term of this series is when
[tex]n = 12[/tex]
[tex]U_ {12}= 3 + 2(12)[/tex]
[tex]U_ {12}= 3 + 24 = 27[/tex]
The sum of the first n terms of an arithmetic series when the first an last term is known is given by:
[tex]S_n = \frac{n}{2}(a + l)[/tex]
Where a=5 is the first term and l=27 is the last term.
[tex]S_ {12} = \frac{12}{2}(5 + 27)[/tex]
[tex]S_ {12} =6(32) =19 2[/tex]
