Question 388654
Two terms of an arithmetic sequence are 
a(9) = 85 and a(30) = 295. 
Find a rule for the nth term.
a(30) = a+29d = 295
a(9)  = a+8d = 85
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Subtract and solve for "d":
21d = 210
d = 10
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Solve for "a":
a+8*d = 85
a = 5
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Therefore: a(n) = 5+(n-1)10 = 5+10n-10 = -5+10n


−5 + 12n 
−5 + 10n 
5 + 10n 
5 + 12n
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Q2) What is the measure of the angle θ in the triangle shown? 
θ 31.07 
θ 58.93 
θ 62.70 
θ 27.30
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Triangle not shown.
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Q3) Solve 3 tan x −√3 = 0.
tan(x) = sqrt(3)/3
x = invtan(sqrt(3)/3) = pi/6 or (7/6)pi
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x = π/6 + nπ 
x = π/6 or x = 7π/6 
x = π/6 + 2nπ 
x = √2 or x = √3
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Q4) 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
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Follow the pattern above to get the answer.
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Q5) MONSTER TRUCKS A monster truck drives off a ramp in order to jump onto a row of cars. The ramp has a height of 8 feet and a horizontal length of 28 feet. What is the angle θ of the ramp? Round your answer to the nearest integer, if necessary.
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invtan(8/28) = 15.95 degrees
θ 16 
θ 14 
θ 12 
θ 10 
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Q6) Solve cos x − 1 = 0 on the interval 0 ≤x ≤ π/2.
x = π/3 
x =0 
x = π/6 
x = π/4 
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Done elsewhere
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Q7) 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
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Done elsewhere
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Q8) What is the measure of the angle θ in the triangle shown? 
θ 63.43 
θ 30.00 
θ 60.00 
θ 26.57 
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Triangle not shown
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Q9) Graph f(x) = sin (x − 2π) − 1. Vertical shift = -1
Vertical shift = -2 
Vertical shift = -1 
Vertical shift = -3 
Vertical shift = 0
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Q10) Two terms of an arithmetic sequence are a7 = 33 and a22 = 138. Find a rule for the nth term.
16 + 10n 
16 + 7n 
−16 + 10n 
−16 + 7n
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Follow the pattern above to get the answer.
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Cheers,
Stan H.