Answer: choice A) 7017
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Work Shown:
The first term is a_1 = 24 and we go up by 7 each time.
The common difference is d = 7
The nth term formula we'll use is
a_n = a_1 + (n-1)*d
a_n = 24 + (n-1)*7
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The 1000th term corresponds to n = 1000
Replace every n with 1000
Then use the order of operations (PEMDAS) to simplify
a_n = 24 + (n-1)*7
a_1000 = 24 + (1000-1)*7
a_1000 = 24 + (999)*7
a_1000 = 24 + 6993
a_1000 = 7017
Theorem of cosine:
a²=b²+c²-2bc(cos α) ⇒cos α=-(a²-b²-c²) / 2bc
In this case:
a=15 cm
b=10 cm
c=5 cm
cos α=-(15²-10²-5²) / 2*10*5
cos α=-100 / 100
cos α=-1
A=arc cos -1=180º This is impossible, because:
A+B+C=180º; then B=C=0º This is impossible for make a triangle (B>0 and C>0 if we want to make a triangle).
Therefore: it is not possible can make a triangle with side lengths of 5 cm, 10 cm and 15 cm.
Every triangle’s inner angles’ addition equals to 180°
So if we find the x:
38°+x+2°+x=180°
40°+2x=180°
2x=180°-40°=140°
x=140°/2
x=70°
Now if we find the I hope this helped :)
