Rita is spending more time at home to study and practice math. Her efforts are finally paying off. On her first assessment she scored 58 points, then she scores 63 and 68 on her next two assessments. If her scores continued to increase at the same rate, on which assessments will she be scoring above 85 ? Select all that apply.
Fourth
Fifth
Sixth
Seventh
Eighth
Ninth
Answer
Solve for \(n\): \(n > 6.4\). So, we find assessments 7, 8, and 9.
Step 1 ：Let the initial score be \(A_1\) and the common difference between the scores be \(d\). Then, \(A_1 = 58, A_2 = 58 + d = 63, A_3 = 58 + 2d = 68\).
Step 2 ：Find the common difference, \(d = A_2 - A_1 = 63 - 58 = 5\).
Step 3 ：Then, find the assessment at which she scores above 85: \(A_n > 85\), where \(A_n = A_1 + (n - 1)d\). Substitute values: \(A_n = 58 + (n - 1)5 > 85\).
Step 4 ：Solve for \(n\): \(n > 6.4\). So, we find assessments 7, 8, and 9.
