Question

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

Answer 1

Answer:

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