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What is the sum of first six terms of a sequence whose nth term is 8 - n?
nth term is 8 - n. an = 8 - n, so the sequence is {7, 6, 5, 4, 3, 2,...} (this is a decreasing sequence since the successor term is smaller than the nth term). So, the sum of first six terms of the sequence is 27.
What is the nth term of the arithmetic sequence 7 5 3 1?
To find the nth term of an arithmetic sequence, you need to first identify the common difference between consecutive terms. In this case, the common difference is -2 (subtract 2 from each term to get the next term). The formula to find the nth term of an arithmetic sequence is: a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference. Plugging in the values from the sequence (a_1=7, d=-2), the nth term formula becomes: a_n = 7 + (n-1)(-2) = 9 - 2n.
Find the quadratic sequences nth term for these 4 sequences which are separated by the letter i iii 7 10 15 22 21 42 iii 2 9 18 29 42 57 iii 4 15 32 55 85 119 iii 5 12 27 50 81 120?
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)
How do you find the nth term in a sequence?
Finding the nth term is much simpler than it seems. For example, say you had the sequence: 1,4,7,10,13,16 Sequence 1 First we find the difference between the numbers. 1 (3) 4 (3) 7 (3) 10 (3) 13 (3) 16 The difference is the same: 3. So the start of are formula will be 3n. If it was 3n, the sequence would be 3,6,9,12,15,18 Sequence 2 But this is not our sequence. Notice that each number on sequence 2 is 2 more than sequence 1. this means are final formula will be: 3n+1 Test it out, it works!
This is Q of sequence series hlp me1 2 4 8 16 ..find nth term of the series find sum of first n term?
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...
How do you work out the 20th term of a sequence?
To find the 20th term of a sequence, first identify the pattern or formula that defines the sequence. This could be an arithmetic sequence, where each term increases by a constant difference, or a geometric sequence, where each term is multiplied by a constant factor. Once the formula is established, substitute 20 into the formula to calculate the 20th term. If the sequence is defined recursively, apply the recursive relation to compute the 20th term based on the previous terms.
What is the sum of the first 28 terms of this arithmetic sequence?
To find the sum of the first 28 terms of an arithmetic sequence, you need the first term (a) and the common difference (d). The formula for the sum of the first n terms (S_n) of an arithmetic sequence is S_n = n/2 * (2a + (n - 1)d). Once you have the values of a and d, plug them into the formula along with n = 28 to calculate the sum.
What is the simple formula corresponding to the explicit formula if the first term of the sequence is -10 and the difference between terms in the sequence is 3?
Assuming each term is 3 MORE than the previous term t(n) = -13 + 3*n where n = 1, 2, 3, ...
What are the first five terms of the sequence whose nth term is N4 plus 225?
2,1,0 is th sequence of its terms
Find the explicit formula for the sequence?
The explicit formula for a sequence is a formula that allows you to find the nth term of the sequence directly without having to find all the preceding terms. To find the explicit formula for a sequence, you need to identify the pattern or rule that governs the sequence. This can involve looking at the differences between consecutive terms, the ratios of consecutive terms, or any other mathematical relationship that exists within the sequence. Once you have identified the pattern, you can use it to create a formula that will generate any term in the sequence based on its position (n) in the sequence.
What are the first four terms of a sequence when the nth term equals 3 to the power of n and what term number is 729 in the sequence?
The first four terms are 3 9 27 81 and 729 is the 6th term.
If the first differences of a sequence are a constant 4 and the second term is 8 what are the first 5 terms of the sequence?
4,8,12,16,20
How do you find the formula for the nth term in a sequence?
To find the formula for the nth term in a sequence, start by identifying the pattern or rule governing the sequence by examining the differences between consecutive terms. If the differences are constant, the sequence is linear; if the second differences are constant, it may be quadratic. Use techniques like polynomial fitting or recursive relationships to derive a general formula. Finally, verify your formula by substituting values of n to ensure it produces the correct terms in the sequence.
Is the explicit rule for a geometric sequence defined by a recursive formula of for which the first term is 23?
Yes, the explicit rule for a geometric sequence can be defined from a recursive formula. If the first term is 23 and the common ratio is ( r ), the explicit formula can be expressed as ( a_n = 23 \cdot r^{(n-1)} ), where ( a_n ) is the nth term of the sequence. This formula allows you to calculate any term in the sequence directly without referencing the previous term.
What is the first three terms whose nth term is given by the formula 2-n?
The nth term of the sequence given by the formula (2 - n) can be found by substituting (n) with the first three positive integers: For (n = 1): (2 - 1 = 1) For (n = 2): (2 - 2 = 0) For (n = 3): (2 - 3 = -1) Thus, the first three terms of the sequence are 1, 0, and -1.
The nth term -4,-1,4,11,20,31?
14112027
What is a finite sequence?
A finite sequence is a list of numbers or elements that has a specific, limited number of terms. Each term in the sequence is typically defined by a particular rule or formula, and the sequence terminates after reaching its last term. Unlike infinite sequences, which continue indefinitely, finite sequences can be fully enumerated and counted. Examples include the sequence of integers from 1 to 10 or the first five terms of a geometric series.
