Algebra 2 Problems of the Day (Jan 2020)

Daily Algebra 2 questions and answers.

More Algebra 2 problems.

January 2020, Part II

All Questions in Part II are worth 2 credits. Work must be shown. Partial credit is given.


29. Given the geometric series 300 + 360 + 432 + 518.4 + ..., write a geometric series formula, S_n, for the sum of the first n terms. Use the formula to find the sum of the first 10 terms, to the nearest tenth.

Answer:
Find the formula for Geometric Series in the back of the booklet:
S_n = (a₁ - a₁rⁿ) / (1 - r), where r is the Common Ratio of the series.
360 / 300 = 1.2
432 / 360 = 1.2, etc.
r = 1.2

S_n = (300 - 300(1.2)¹⁰) / (1 - 1.2) = 7787.6...
S₁₀ = 7787.6

30. Visible light can be represented by sinusoidal waves. Three visible light waves are shown in the graph below. The midline of each wave is labeled L.

Based on the graph, which light wave has the longest period? Justify your answer.

Answer:
Check the length between maximum and minimum.
A has a max at 60 and a min at 340. 340 - 60 = 280
B has a max at 180 and a min at 400. 400 - 180 = 220
C has a max at 380 and a min at 60. 380 - 60 = 320.
Light wave C has the longest period.

Comments and questions welcome.

More Algebra 2 problems.