Since the sequence is arithmetic, we have an expression of the form:
[tex]an = a1 + d (n-1)
[/tex]
Where,
a1: first term of the sequence
d: common difference
n: number of terms
We look for the common difference:
[tex]d = 22-15 = 15-8 = 7
d = 7[/tex]
Then, setting values we have:
[tex]a26 = 8 + 7 * (26-1)
a26 = 183
[/tex]
Then, the sum of the terms is:
[tex]Sn = ((a1 + an) / (2)) * n
[/tex]
Substituting values:
[tex]Sn = ((8 + 183) / (2)) * 26
Sn = 2483[/tex]
Answer:
the sum of the arithmetic sequence 8, 15, 22 is:
Sn = 2483
