Answer:
sum of the first 27 terms = -1431
Step-by-step explanation:
arithmetic series sum of the first n terms formula:
[tex] s_{n} = \frac{n}{2} (2a + (n - 1)d)[/tex]
n = 27 terms
first term, a = 25
common difference, d = 19 - 25 = -6
substitute the values into the formula
[tex] s_{27} = \frac{27}{2} (2(25) + (27 - 1)( - 6))[/tex]
[tex] s_{27} = 13.5(50 + 26( - 6))[/tex]
[tex] s_{27} = 13.5(50 - 156)[/tex]
[tex] s_{27} = 13.5( - 106)[/tex]
[tex]s_{27} = - 1431[/tex]
