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consider the sequence:

5, 7, 11, 19,

write an explicit definition that defines the sequence:

group of answer choices

a_n=2n+3 a n = 2 n + 3

a_n=3n+2 a n = 3 n + 2

a_n=3n^2 a n = 3 n 2

a_n=2^n+3

1st answer is d, 2nd answer is d ,3rd answer is d, 4th answer is c,5th answer is c and 6th answer is c

Step-by-step explanation:

        we get the series 2,4,8,16

        The general term for first difference GP we have an=c×2∧n+d

        by  putting n=1 we get 5=2c+d and by n=2 we get 7=4c+d

        By solving the two equations we get c=1 and d=3

         an=2∧n+3

    2. tn+1= -1×tn+3

        By analysis the option we get tn=4 then we tn+1=-1  so only d option

       satisfy the condition rest options don't satisfy so answer is option d                    

    3. Given t1=5 and the condition is given that tn+1=3×tn

        putting n=1 we get t2=3×t1  

      ∵By substituting we get t2=3×5=15

   4. The sequence is given as 8,11,14,17,20,23,26

       This is an A.P. so the general term of A.P. is given as tn=t(n-1)+d

       where t(n-1)is the previous  term and d is the common difference which

       is equal to 3 in this case

       ∵The answer is tn=t(n-1)+3

   5.The sequence is given as 5,8,11,14,17 we have to find

       the 43rd term of the sequence  

       The given sequence is an A.P.

       ∵The general term is an=a+(n-1)d where a is the first term and d be

       the common difference which is equal to 3 in this case

       We have to find the 43rd term so n=43

       By substituting in the given equation we get a43=5+(43-1)×3=129

       ∴The 43rd term of the given sequence is equal to  129

  6. When we count the boxes we get that they follow a pattern given as

      1,5,9,13 This follow an series of A.P.

      ∵ The general term is an=a+(n-1)d where a is the first term and d be the      

      common difference which is equal to 4 in this case

       we have to find the number of boxes in 10th step of pattern so n=10 for        

        case a10=1+(10-1)×4=37

      ∴The number of boxes in the 10th step is 37

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation:

7 is the median   7.875 is the mean

step-by-step explanation:

3,4,5,6,8,11,13,13