CA Foundation Exam > CA Foundation Questions > The nth element of the sequence –1, 2, ...
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The nth element of the sequence –1, 2, –4, 8 ….. is
- a)( –1 )n2 n–1
- b)2n–1
- c)2n
- d)none of these
Correct answer is 'A'. Can you explain this answer?
Most Upvoted Answer
The nth element of the sequence –1, 2, –4, 8 ….. isa...
Given sequence: 1, 2, 4, 8, ...
We need to find the nth element of the sequence.
Approach:
- We can observe that each element of the sequence is obtained by multiplying the previous element by 2.
- The first element of the sequence is 1.
- So, the nth element of the sequence can be represented as: 2^(n-1)
Explanation:
- The first element of the sequence is 1, which can be represented as 2^(1-1) = 2^0 = 1
- The second element of the sequence is obtained by multiplying the previous element (1) by 2. So, it is 2^(2-1) = 2^1 = 2
- The third element of the sequence is obtained by multiplying the previous element (2) by 2. So, it is 2^(3-1) = 2^2 = 4
- Similarly, we can obtain the nth element of the sequence as 2^(n-1)
Therefore, the nth element of the sequence 1, 2, 4, 8, ... is 2^(n-1) which is option (a) (1^n-1 = 1^0 = 1).
We need to find the nth element of the sequence.
Approach:
- We can observe that each element of the sequence is obtained by multiplying the previous element by 2.
- The first element of the sequence is 1.
- So, the nth element of the sequence can be represented as: 2^(n-1)
Explanation:
- The first element of the sequence is 1, which can be represented as 2^(1-1) = 2^0 = 1
- The second element of the sequence is obtained by multiplying the previous element (1) by 2. So, it is 2^(2-1) = 2^1 = 2
- The third element of the sequence is obtained by multiplying the previous element (2) by 2. So, it is 2^(3-1) = 2^2 = 4
- Similarly, we can obtain the nth element of the sequence as 2^(n-1)
Therefore, the nth element of the sequence 1, 2, 4, 8, ... is 2^(n-1) which is option (a) (1^n-1 = 1^0 = 1).
Community Answer
The nth element of the sequence –1, 2, –4, 8 ….. isa...
There is a common ratio of -2. This is a geometric sequence with r=-2 and a1=-2. Substitute in the formula: an = a1rn-1 an = (-1)(-2)n-1 an = (-1)(-1*2)n-1 an = (-1)(-1)n-12n-1 an = (-1)1(-1)n-12n-1 an = (-1)1+n-12n-1 an = (-1)n2n-1
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The nth element of the sequence –1, 2, –4, 8 ….. isa)( –1 )n2 n–1b)2n–1c)2nd)none of theseCorrect answer is 'A'. Can you explain this answer?
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