Question

1. the first five terms of a sequence are shown below.

101, 92, 83, 74, 65, ...
based on this information, create an equation that can be used to find the ( n^{\text{th}} ) term of the sequence, ( a_n ). then, use the equation to find ( a_{35} ).
equation: ( a_n = square )
( a_{35} = square )

Explanation:

Step1: Identify sequence type (Arithmetic)

Check difference: \(92 - 101 = -9\), \(83 - 92 = -9\), so common difference \(d = -9\), first term \(a_1 = 101\).

Step2: Arithmetic sequence formula

Arithmetic sequence formula: \(a_n = a_1 + (n - 1)d\). Substitute \(a_1 = 101\), \(d = -9\):
\(a_n = 101 + (n - 1)(-9)\)
Simplify: \(a_n = 101 - 9n + 9 = 110 - 9n\).

Step3: Find \(a_{35}\)

Substitute \(n = 35\) into \(a_n = 110 - 9n\):
\(a_{35} = 110 - 9(35)\)
Calculate: \(110 - 315 = -205\).

Answer:

Equation: \(a_n = 110 - 9n\)
\(a_{35} = -205\)