- #1
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Homework Statement
Problem 1:
Two Arithmetic Sequences are given.
[lat]a_n = 200,196,192,188,184...[/lat]
[ltaex]b_n = 100,103,106,109,112...[/itex]
For integers l,m, find the number of pairs consisting of (l,m) which satifies condition [itex]a_l = b_m[/itex]
Problem 2:
Three terms, sin(x), sqrt(3)/4, cos(x) form an arithmetic sequence. Find 2 |tan(x) + 1/tan(x)|
Homework Equations
[itex] a_n = a + (n-1)d[/itex]
The Attempt at a Solution
For problem 1:
The equations formed for both arithmetic sequences are
[itex]a_n = -4n + 204[/itex]
[itex]b_n = 3n + 97[/itex]
I thought about making them equal to find the exact n which both a_n and b_n is equal of but I'm pretty sure that's not the correct way to do it. What should I do?
And for Problem 2:
since three terms are in incremental sequence, we can find that
sqrt(3)/4 = (sin(x) + cos(x)) / 2
which yields
sqrt(3)/2 = sin(x) + cos(x)
I feel like I need to do something with trigonometric identity to substitute that, so I tried:
2|tan^2(x) + 1 / tan(x)|
= 2|sec^2(x) / tan(x)|
= 2|1/cos(x)(sin(x)|
which didn't get me anywhere.
Any suggestions?
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