Calculate s5 for the sequence defined by

ANSWER

[tex]S_5= 42.5[/tex]

EXPLANATION

The general term of the arithmetic sequence is

[tex]a_n=1+\frac{5}{2}n[/tex]

For the first term,we substitute [tex]n=1[/tex] to get,

[tex]a_1=1+\frac{5}{2}\times 1[/tex]

[tex]a_1=1+2.5=3.5[/tex]

Similarly

[tex]a_5=1+\frac{5}{2}\times 5[/tex]

[tex]a_5=13.5[/tex]

The sum of the first n-terms is given by the formula,

[tex]S_n=\frac{n}{2}(a_1+l)[/tex]

where l is the last term.
In this case

[tex]l=a_5=13.5[/tex]

We substitute these values to get,

[tex]S_5= \frac{5}{2} (3.5 + 13.5)[/tex]

[tex]S_5= \frac{5}{2} (17)[/tex]
[tex]S_5=42.5[/tex]

We could have also used the formula,

[tex]S_n=\frac{n}{2}(2a_1+(n-1)d)[/tex]

[tex]S_5=\frac{5}{2}(2(3.5)+(5-1)2.5)[/tex]

[tex]S_5=42.5[/tex]

netflixacc0107 netflixacc0107 · Answer 2 · 2018-12-10T03:34:24+01:00

netflixacc0107 netflixacc0107

10-12-2018

Answer:

42.5 is the one

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