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(1+n) x n/2 or (n + n2)/2
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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)
What shape has 7 faces 15 edges and 10 verticels?
A pentagonal prism has 7 faces, 15 edges and 10 vertices
What is the 100th and nth term out of 5 7 9 11 13 15 17?
Any number that you choose can be the 100th or nth number. It is easy to find a rule based on a polynomial of order 7 such that the first seven numbers are as listed in the question followed by the chosen next number in the 100th place. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.However, the simplest solution here ist(n) = 2n + 3 for n = 1, 2, 3, ...and so t(100) = 203.
A packing box is 15 inches long 12 inches wide and 10 inches tall what is the surface area of the packing box?
2x((15*12)+(15*10)+(12*10)) is 2*(180+150+120) = 900in2
The area of a triangle with a base of 10 centimeters and a height of 15 centimeters?
(1/2)base*height = .5(10)(15) = 75
What is the nth term for 7 11 15 19?
The nth term in this sequence is 4n + 3.
What is the nth term if the sequence is 22 15 8 1 -6?
It is: nth term = 29-7n
What is the nth term for 151173?
If you mean: 15 11 7 3 then the nth term is 19-4n
What is the nth term for 7 10 15 22 31 42?
Type your answer here... The next numbers in the sequence are 55, 70, 87, 106, 127, etc.
What is the nth term of the sequence 15 25 35 45 55?
15(1)
Which of the following best completes the sequence 5 10 15 20?
The nth term is: 5n
What is the nth term of 1 -3 -7 -11 and -15?
It is: nth term = 5-4n and so the next term will be -19
What is the nth term in the sequence 3 7 11 15?
The nth term is 4n-1 and so the next term will be 19
What is the nth term of 15 12 9 6.?
The nth term is 18 -3n and so the next term will be 3
What is the nth term in 1 3 7 11 15?
If you mean -1 3 7 11 15 then the nth term is 4n-5 and so the next term will be 19
How do you find the nth term?
Say if you had the pattern 15 20 25 30 35 40 45 50 To find the nth term you have to see what the gap between the numbers is. In our case this is 5. Then you have to find out what the difference between the gap and the first number. In this sequence it is 10. So your answer would be..... 5n+10 That's how you find the nth term.
What is the nth term of the arithmetic sequence 22 15 8 1 ...?
The nth term is -7n+29 and so the next term will be -6
