Consider the sequence -101, -91, -81, -71, ...Determine an explicit formula for the nth term of the sequence

Answer: [tex]t_{n}[/tex] = 10n - 111Step-by-step explanation:The first term of the sequence is - 101we need to confirm that the sequence is arithmetic , that is , if it is arithmetic , it must have a common difference (d).d = second term - first term = third term - second termd = -91 - (-101)d = -91 + 101d = 10Therefore the formula for the nth term is given as:[tex]t_{n}[/tex]= a + (n - 1 ) d[tex]t_{n}[/tex] = - 101 + (n - 1) 10[tex]t_{n}[/tex] = - 101 + 10n - 10[tex]t_{n}[/tex] = -111 + 10nTherefore :[tex]t_{n}[/tex] = 10n - 111