The sum of the arithmetic sequence. 17, 19, 21, 23, ..., 35 is 260.
What is the sum of arithmetic series?
The sum of terms in any series is the result of the addition of the first terms in that series.
The given arithmetic sequence is;
17, 19, 21, 23, ..., 35
The sum of the arithmetic sequence is given by the following formula;
[tex]\rm S_n=\dfrac{n}{2}(a_1+a_n)\\\\Where; \ a_1 = first \ term , \ a_n = last \ term[/tex]
The total number of terms is given by;
[tex]\rm a_n=a+(n-1)d\\\\35 = 17+(n-1)2\\\\35-17=(n-1)2\\\\ \dfrac{18}{2}=n-1\\\\9=n-1\\\\n=9+1\\\\n=10[/tex]
Substitute all the values in the formula
[tex]\rm S_n=\dfrac{n}{2}(a_1+a_n)\\\\ S_n=\dfrac{10}{2}(17+35)\\\\ S_n=5 \times 52\\\\S_n=260[/tex]
Hence, the sum of the arithmetic sequence. 17, 19, 21, 23, ..., 35 is 260.
Learn more about arithmetic sequence here;
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