For !

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

47 - 90 = 43

43 - 180 = x

x = 137