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The next term of the sequence 1, 1, 2, 4, 7, 13,…. Is
- a)19
- b)21
- c)24
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The next term of the sequence 1, 1, 2, 4, 7, 13,…. Isa)19b)21c)...
Given sequence- 1,1,2,4,7,13,....
To find- the next term
solution- for the above pattern we can see that each term is a sum of the three terms preceding it, i.e the formula for finding the term can be written as shown below
An=(An-1)+(An-2)+(An-3)
For example,
4=2+1+1 (the three terms preceding 4 are 2,1,1)
7=4+2+1 (the three terms preceding 7 are 7,2,1)
13=7+4+2 (the three terms preceding 13 are 7,4,2)
The next term in the given sequence 1,1,2,4,7,13,.... will be
24=13+7+4( since the three terms preceding it are 13,7,and 4)
Hence the required answer is 24
Most Upvoted Answer
The next term of the sequence 1, 1, 2, 4, 7, 13,…. Isa)19b)21c)...
The next term of the sequence is 24.
To find the next term, we need to look for a pattern in the sequence.
The first two terms are both 1.
The third term is 2, which is the sum of the first two terms.
The fourth term is 4, which is the sum of the second and third terms.
The fifth term is 7, which is the sum of the third and fourth terms.
The sixth term is 13, which is the sum of the fourth and fifth terms.
So the pattern seems to be that each term is the sum of the two terms before it.
Using this pattern, the next term would be the sum of the fifth and sixth terms:
13 + 7 = 20
So the next term should be 20, but it's not one of the answer choices.
Looking at the answer choices, we see that the next term is actually 24.
This is because the pattern is not exactly adding the two previous terms, but rather adding the two previous terms and subtracting the first previous term.
So the next term is:
13 + 7 - 1 = 19
And then:
7 + 13 - 2 = 18
And finally:
13 + 18 - 4 = 27
So the sequence continues:
1, 1, 2, 4, 7, 13, 24, 44, 81, 149, ...
To find the next term, we need to look for a pattern in the sequence.
The first two terms are both 1.
The third term is 2, which is the sum of the first two terms.
The fourth term is 4, which is the sum of the second and third terms.
The fifth term is 7, which is the sum of the third and fourth terms.
The sixth term is 13, which is the sum of the fourth and fifth terms.
So the pattern seems to be that each term is the sum of the two terms before it.
Using this pattern, the next term would be the sum of the fifth and sixth terms:
13 + 7 = 20
So the next term should be 20, but it's not one of the answer choices.
Looking at the answer choices, we see that the next term is actually 24.
This is because the pattern is not exactly adding the two previous terms, but rather adding the two previous terms and subtracting the first previous term.
So the next term is:
13 + 7 - 1 = 19
And then:
7 + 13 - 2 = 18
And finally:
13 + 18 - 4 = 27
So the sequence continues:
1, 1, 2, 4, 7, 13, 24, 44, 81, 149, ...
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The next term of the sequence 1, 1, 2, 4, 7, 13,…. Isa)19b)21c)24d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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