a. The next four terms are 5/10, -6/11, 7/12, -8/13.
b. The explicit equation for f (n) is f(n) = (-1)ⁿ × (n+1)/(n+6) , n = 0,1,2,3...
c. If n = 53, then (-1)ⁿ = (-1)⁵³ = -1. so, f(n) is negative.
What is the explicit equation?
Without expressing the other terms of the sequence, explicit formulas are always utilized to represent any term of the sequence. The word "explicit" means something that may be found directly without having to know the other phrases in the sequence. A single formula, known as the explicit formula, can be used to describe each term in a series in an individual way.
Explicit formulas of different sequences:
Arithmetic Sequence: aₙ = a + (n - 1) d,
Geometric Sequence: aₙ = a× r^(n - 1),
Harmonic Sequence: aₙ = 1 / [a + (n - 1) d].
Here. we have
Given sequence 1/6, -2/7, 3/8, -4/9
a. The next four terms are 5/10, -6/11, 7/12, -8/13.
b. The explicit equation for f (n) is f(n) = (-1)ⁿ × (n+1)/(n+6) , n = 0,1,2,3...
c. If n = 53, then (-1)ⁿ = (-1)⁵³ = -1. so, f(n) is negative.
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