Question: an arithmetic sequence is a sequence with a common difference. it can be represented by the recursive formula a1 = a (where a is the first term of the sequence); an = an - 1 + d. a) create your own arithmetic sequence. write out the first 3 terms. b) what is the common difference of your sequence? c) write the recursive formula representing your sequence. use the underscore symbol to indicate a subscript. for example, the recursive formula would be written like a1 = a; a_n = a_(n – 1) + d

a) 3,6,9,12,15,..

b) Common Ratio is 3

c) Recursive Formula : aₙ= aₙ₋₁ + d where a₁=3 and d= 3

Step-by-step explanation:

a) Create your own arithmetic sequence. Write out the first 3 terms.

Consider the sequence: 3,6,9,12,15,..

a₁ = 3

a₂ = 6

a₃ = 9

b) What is the common difference of your sequence?

6-3 = 3

9-6 = 3

12 -9 =3

So, common difference is 3

c) Write the recursive formula representing your sequence.

a₁ = 3

a₂ = aₙ₋₁ + d

   = a₁ + d

   = 3+ 3 = 6

a₃ = aₙ₋₁ + d

    = a₂ + d

   = 6+3 = 9

so, recursive formula is aₙ = aₙ₋₁ + d where a₁ = 3 and d= 3

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation: