Find the 50th term of this arithmetic sequence: 6, 13, 20, 27, . . .
1 answer:
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Answer:
Step-by-step explanation:
Given points P(1, -1, 4), Q (4,2,1) vector equation of a line joining the points with position vectors r₀ and r₁ is:
r = (1 - t)r₀ + tr₁
where
t ∈ [0, 1]
and r₀ = P = (1, -1, 4)
r₁ = Q = (4, 2, 1)
r(t) = (1 - t) + t
∴
The vector equation where t ∈ [0,1] is:
r(t) = (1+3t)i - (1+3t)j + (4 - 3t)k
The parametric equation is:
x(t) = 1 + 3t
y(t) = -1 + 3t
z(t) = 4 - 3t
(x(t), y(t), z(t) ) = ( 1 + 3t, -1 + 3t, 4 - 3t )