Arithmetic Series in Real Life: Grade 11 Practice

Maya saves $20 in January, $25 in February, $30 in March, and increases her savings by $5 each month. How much money will she save in total over 12 months?

a1 = 20, d = 5, n = 12. S12 = (12 / 2)(2(20) + (12 - 1)5) = 6(40 + 55) = 6(95) = $570.

An amphitheater has 22 seats in the first row and 58 seats in the 10th row. If the seating increases evenly in each row, how many total seats are in the first 10 rows?

a1 = 22, a10 = 58, n = 10. S10 = (10 / 2)(22 + 58) = 5(80) = 400 seats.

A runner completes 4 miles on day one and increases the distance by 1.5 miles each day. On which day will the runner reach a cumulative total of 35 miles?

a1 = 4, d = 1.5, Sn = 35. 35 = (n / 2)(2(4) + (n - 1)1.5) leads to 1.5n^2 + 6.5n - 70 = 0, or 3n^2 + 13n - 140 = 0. Factoring gives (3n + 28)(n - 5) = 0. Discarding the negative root gives n = 5 days.

A company lays off workers in phases to reduce staff. They release 8 workers the first week, 12 the second week, and 16 the third week. How many total workers are released across 8 weeks?

a1 = 8, d = 4, n = 8. S8 = (8 / 2)(2(8) + (8 - 1)4) = 4(16 + 28) = 4(44) = 176 workers.

A pile of logs has 30 logs in the bottom row, 29 in the next, and each row has 1 fewer log than the row below it. If the pile contains 380 logs in total, how many rows are in the pile?

a1 = 30, d = -1, Sn = 380. 380 = (n / 2)(2(30) + (n - 1)(-1)) leads to n^2 - 61n + 760 = 0. Factoring gives (n - 19)(n - 40) = 0. Because a row cannot contain negative logs, n = 40 is invalid (a40 = 30 - 39 = -9 logs). Thus, n = 19 rows.