Answer:
2n² + n
Step-by-step explanation:
<u>Given sequence</u>:
3, 10, 21, 36, ...
Work out the first differences between terms:
![3 \underset{+7}{\longrightarrow} 10 \underset{+11}{\longrightarrow} 21 \underset{+15}{\longrightarrow} 36](https://tex.z-dn.net/?f=3%20%5Cunderset%7B%2B7%7D%7B%5Clongrightarrow%7D%2010%20%5Cunderset%7B%2B11%7D%7B%5Clongrightarrow%7D%2021%20%5Cunderset%7B%2B15%7D%7B%5Clongrightarrow%7D%2036)
As the <u>first differences</u> are <em>not </em>the same, work out the second differences.
![7 \underset{+4}{\longrightarrow} 11 \underset{+4}{\longrightarrow} 15](https://tex.z-dn.net/?f=7%20%5Cunderset%7B%2B4%7D%7B%5Clongrightarrow%7D%2011%20%5Cunderset%7B%2B4%7D%7B%5Clongrightarrow%7D%2015)
As the second differences are the <u>same</u>, the sequence is quadratic and will contain an n² term.
The coefficient of n² is always <u>half of the second difference</u>. Therefore, as the second difference is 4, the coefficient of n² is 2.
To work out the nth term of the sequence, write out the numbers in the sequence 2n² and compare with the given sequence:
![\begin{array}{|l|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4 \\\cline{1-5} 2n^2 & 2 & 8 & 18 & 32\\\cline{1-5} \sf Operation & +1 & +2& +3& +4\\\cline{1-5} \sf Sequence & 3 & 10 & 21 & 36\\\cline{1-5}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7B%7Cl%7Cc%7Cc%7Cc%7Cc%7C%7D%5Ccline%7B1-5%7D%20n%20%26%201%20%26%202%20%26%203%20%26%204%20%5C%5C%5Ccline%7B1-5%7D%202n%5E2%20%26%202%20%26%208%20%26%2018%20%26%2032%5C%5C%5Ccline%7B1-5%7D%20%5Csf%20Operation%20%26%20%2B1%20%26%20%2B2%26%20%2B3%26%20%2B4%5C%5C%5Ccline%7B1-5%7D%20%5Csf%20Sequence%20%26%203%20%26%2010%20%26%2021%20%26%2036%5C%5C%5Ccline%7B1-5%7D%5Cend%7Barray%7D)
Therefore, we need to add n to 2n² to match the sequence.
Therefore, the nth term of this sequence is 2n² + n.
Learn more about sequences here:
brainly.com/question/27953040
brainly.com/question/27775450
The answer for possible rational zero g to f is : x , 1,-1,2,-2,4,-4,8,-8,16,-16
The answer for rational zeros x= -2,2,4
The answer for question 2 : zero: 1,1/2,-1/2, 2
The answer for question 4 : zero: 0,1,-6
You can divide the polygon into a triangle (VMR) and rectangle(VEDR)
VE=5
VR=6
The area for VEDR would be:
area= VE*VR= 5*6= 30
triangle height=3
VR=6
The area for VMR
area= 1/2 * 3 * 6= 9
Total area= 30 + 9 = 39
Answer:
3rd option
Step-by-step explanation:
The sum to infinity of a geometric sequence is
S = ![\frac{a}{1-r}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B1-r%7D)
where a is the first term and r the common ratio
The expression inside the summation is
6 ![(\frac{1}{3}) ^{n-1}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B3%7D%29%20%5E%7Bn-1%7D)
which is in the form of the nth term of a geometric sequence
with a = 6 and r =
, then
S =
← expression required
= ![\frac{6}{\frac{2}{3} }](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B%5Cfrac%7B2%7D%7B3%7D%20%7D)
= 9
Https://www.education.com/activity/article/Size_Your_Stuffed_Animal/
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