Since there are no graphs following, the answer is none of them.
Graph D
Check if the given sequences are quadratic sequences. 7 10 15 22 21 42 The first difference: 3 5 7 1 21. The second difference: 2 2 6 20. Since the second difference is not constant, then the given sequence is not a quadratic sequence. 2 9 18 29 42 57 The first difference: 7, 9, 11, 13, 15. The second difference: 2 2 2 2. Since the second difference is constant, then the given sequence is a quadratic sequence. Therefore, contains a n2 term. Let n = 1, 2, 3, 4, 5, 6, ... Now, let's refer the n2 terms as, 1, 4, 9, 16, 25, 36. As you see, the terms of the given sequence and n2 terms differ by 1, 5, 9, 13, 17, 21 which is an arithmetic sequence,say {an} with a common difference d = 4 and the first term a = 1. Thus, the nth term formula for this arithmetic sequence is an = a + (n - 1)d = 1 + 4(n - 1) = 4n - 3. Therefore, we can find any nth term of the given sequence by using the formula, nth term = n2 + 4n - 3 (check, for n = 1, 2, 3, 4, 5, 6, ... and you'll obtain the given sequence) 4 15 32 55 85 119 The first difference: 11, 17, 23, 30, 34. The second difference: 6 6 7 4. Since the second difference is not constant, then the given sequence is not a quadratic sequence. 5 12 27 50 81 120 The first difference: 7, 15, 23, 31, 39. The second difference: 8 8 8 8. Since the second difference is constant, then the given sequence is a quadratic sequence. I tried to refer the square terms of sequences such as n2, 2n2, 3n2, but they didn't work, because when I subtracted their terms from the terms of the original sequence I couldn't find a common difference among the terms of those resulted sequences. But, 4n2 works. Let n = 1, 2, 3, 4, 5, 6, ... Now, let's refer the 4n2 terms as, 4, 16, 36, 64, 100, 144. As you see, the terms of the given sequence and 4n2 terms differ by 1, -4, -9, -14, -19, -24 which is an arithmetic sequence, say {an} with a common difference d = -5 and the first term a = 1. Thus, the nth term formula for this arithmetic sequence is an = a + (n - 1)d = 1 -5(n - 1) = -5n + 6. Therefore, we can find any nth term of the given sequence by using the formula, nth term = 4n2 - 5n + 6 (check, for n = 1, 2, 3, 4, 5, 6, ... and you'll obtain the given sequence)
If you remember taking sequences, you'll recall that there are three main types: 1)Arithmetic Sequence 2)Geometric Sequence 3)Varied-formula Sequence If the difference between the terms is additional or subractional then its an arithmetic sequence, lets check if this is the case, subtract the first term from the second and the second from the third etc : 1, 2, 4, 8, 16 2-1=1 4-2=2 8-4=4....all the answers are not constant so it is not an arithmetic sequence In a geometric sequence, the difference is in multiplication or division so we divide like this t2/t1 then t3/t2 and then t4/t3 and so on: 2/1=2 4/2=2 8/4=2...all the numbers are constant so this sequence we have here is a geometric sequence to find the nth term we use a formula it varies from the kind of sequence you are using, the formula for a geometric sequence is: tn=t1*r^(n-1) The formula might look confusing so ill write it down for you: "term n= term 1 multiplied by common ratio to the power n-1" The 'common ratio' is the constant so in this case it equals 2. tn=1*2^(n-l) that is the farthest you can go, if the question gives you the nth term then you may substitute it yourself. You didn't make yourself very clear with the last part of your question...
A single number does not constitute a sequence.
The ratio is 4.
It is 0.2
The sequence is neither arithmetic nor geometric.
It appears to be -6
arithmetic sequence
The common difference is the difference between two numbers in an arithmetic sequence.
45, 39, 33, 27, 21, ...
A single term, such as 51474339 does not define a sequence.
It is the "common difference".It is the "common difference".It is the "common difference".It is the "common difference".
yes. A zero common difference represents a constant sequence.
You subtract any two adjacent numbers in the sequence. For example, in the sequence (1, 4, 7, 10, ...), you can subtract 4 - 1, or 7 - 4, or 10 - 7; in any case you will get 3, which is the common difference.
An excellent example of an arithmetic sequence would be: 1, 5, 9, 13, 17, in which the numbers are going up by four, thus having a common difference of four. This fulfills the requirements of an arithmetic sequence - it must have a common difference between all numbers.
It is the difference between a term (other than the second) and its predecessor.
An arithmetic sequence.