a) a(-1)^n-1
b) (-a)^n
c) (-1)a^n+1
Which of the following is the general term for the sequence a, -a, a, -a, . . .?
2016-07-31 6:21 pm
回答 (3)
2016-07-31 6:26 pm
T(1) = a = a (-1)¹⁻¹
T(2) = -a = a (-1)²⁻¹
T(3) = a = a (-1)³⁻¹
T(4) = -a = a (-1)⁴⁻¹
Hence, the general term, T(n) = a (-1)ⁿ⁻¹
...... The answer: a) a (-1)ⁿ⁻¹
T(2) = -a = a (-1)²⁻¹
T(3) = a = a (-1)³⁻¹
T(4) = -a = a (-1)⁴⁻¹
Hence, the general term, T(n) = a (-1)ⁿ⁻¹
...... The answer: a) a (-1)ⁿ⁻¹
2016-07-31 10:01 pm
Answer is: a) a (-1)^n-1
Solution :
If n=1, then a (-1)^n-1 = a (-1)^1-1 = a (-1)^0 = a.1 = a
If n=2, then a (-1)^n-1 = a (-1)^2-1 = a (-1)^ = a.(-1) = -a
If n=3, then a (-1)^n-1 = a (-1)^3-1 = a (-1)^2 = a.1 = a
.......................
So the answer a (-1)^n-1 is correct.
Solution :
If n=1, then a (-1)^n-1 = a (-1)^1-1 = a (-1)^0 = a.1 = a
If n=2, then a (-1)^n-1 = a (-1)^2-1 = a (-1)^ = a.(-1) = -a
If n=3, then a (-1)^n-1 = a (-1)^3-1 = a (-1)^2 = a.1 = a
.......................
So the answer a (-1)^n-1 is correct.
2016-07-31 6:26 pm
a.
You need the n-1 to make the first term positive.
-a, a, -a, a is (-a)^n
You need the n-1 to make the first term positive.
-a, a, -a, a is (-a)^n
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