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Topic: How to write a sequence in math
June 21, 2019 / By Charlton
Question: Two terms of an arithmetic sequence are a8 = 76 and a28 = 296. Find a rule for the nth term. −12 + 11n 12 + 13n 12 + 11n −12 + 13n Q2) Solve 3 tan x −√3 = 0. x = π/6 + nπ x = π/6 or x = 7π/6 x = π/6 + 2nπ x = pm√2 or x = pm√3 Q3) Describe the pattern, write the next term, and write a rule for the nth term of the sequence 5, 5.3, 5.6, 5.9. . . What is the next term in the pattern? The next term in the pattern is 5.9 6.5 6.9 6.2 Q4) Solve 2 sin x − 1 = 0. x =pi/6 or x= 5pi/6 x = pi/6+2npi or x = 5pi/6+2npi x = 2npi x = pm√2 or x = pm√3 Q5) Write 0.555. . . as a fraction in lowest terms. 5/9 6/9 7/9 8/9 Q6) Monster Trucks, A monster truck drives off a ramp in order to jump onto a row of cars. The ramp has a height of 10 feet and a horizontal length of 26 feet. What is the angle θ of the ramp? Round your answer to the nearest integer, if necessary. θ approx24degree θ approx22degree θ approx21degree θ approx23degree Q7) Graph y = 5 sin 4x + 9. The amplitude is ? The amplitude = 5 The amplitude = 10 The amplitude = 15 The amplitude = 20 Q8) RETAIL DISPLAYS You work in a grocery store and you are stacking apples in the shape of a square pyramid with 5 layers. How many apples are in the stack? There are apples in the stack. 55 45 35 30

Alven | 2 days ago
(1) a28 - a8 = 296-76=220. As this is an arithmetic series, this value is 20 times (28-8) the ratio, so the ratio is 220/20 = 11. So a8 = a + 11*8 and therefore 76=a+88 and a=-12. THe general form is therefore -12+11n (2) tan x = (sqrt(3))/3 so x = pi/6 + n pi (3) Every term adds 0.3 to the previous one so tn = 5 + 0.3 (n-1) and the next term is 6.2 (4) sin x = 1/2 and so x is pi/6 or pi-pi/6 = 5 pi/6 (5) 0.555... = 5 (1/10 + (1/10)^2 + (1/10)^3 + ...) = 5 (1/10) / ( 1 - 1/10) = 5/9 (6) sin θ = 10/26 so θ=22.62 degrees i.e. approximately 23 degrees (7) The amplitude is 5 (8) The total number of apples is 1+4+9+16+25 = 55
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(1) a28 - a8 = 296-76=220. As this is an arithmetic series, this value is 20 times (28-8) the ratio, so the ratio is 220/20 = 11. So a8 = a + 11*8 and therefore 76=a+88 and a=-12. THe general form is therefore -12+11n (2) tan x = (sqrt(3))/3 so x = pi/6 + n pi (3) Every term adds 0.3 to the previous one so tn = 5 + 0.3 (n-1) and the next term is 6.2 (4) sin x = 1/2 and so x is pi/6 or pi-pi/6 = 5 pi/6 (5) 0.555... = 5 (1/10 + (1/10)^2 + (1/10)^3 + ...) = 5 (1/10) / ( 1 - 1/10) = 5/9 (6) sin θ = 10/26 so θ=22.62 degrees i.e. approximately 23 degrees (7) The amplitude is 5 (8) The total number of apples is 1+4+9+16+25 = 55