the first 4 terms of the sequence which has the nth term is a sequence of numbers that that goe together eg. 8,12,16,20,24 the nth term would be 4n+4
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.
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.
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)
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!
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...
Assuming each term is 3 MORE than the previous term t(n) = -13 + 3*n where n = 1, 2, 3, ...
2,1,0 is th sequence of its terms
The first four terms are 3 9 27 81 and 729 is the 6th term.
4,8,12,16,20
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.
14112027
In this case, 22 would have the value of 11.
Depends on the sequence. There may be a formula for the Nth term in which case it is easy. Or the value may depend on some combination of previous terms (as in the Fibbonaci series).
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.
To find the sum of the first 48 terms of an arithmetic sequence, we can use the formula for the sum of an arithmetic series: Sn = n/2 * (a1 + an), where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term. In this case, a1 = 2, n = 48, and an = 2 + (48-1)*2 = 96. Plugging these values into the formula, we get: S48 = 48/2 * (2 + 96) = 24 * 98 = 2352. Therefore, the sum of the first 48 terms of the given arithmetic sequence is 2352.
Oh, dude, you're hitting me with the math questions, huh? So, the formula for finding the nth term of an arithmetic sequence is a + (n-1)d, where a is the first term and d is the common difference. In this sequence, the common difference is 8 (because each term increases by 8), and the first term is 14. So, the formula for the nth term would be 14 + 8(n-1). You're welcome.
t(n) = 12*n + 5