Respuesta :

Answer:

a1 = 2; an = a(n-1) + 3/2

Step-by-step explanation:

Common difference = 7/2 - 2

= 7/2 - 4/2

= 3/2  

(Also 5 - 7/2 = 3/2.)

First term a1 = 2

So the formula is  a1 = 2; an = a(n-1) + 3/2 which is the first choice.

The recursive formula for the arithmatic sequence is a₁ = 2, aⁿ = aⁿ⁻¹ + 3/2.

What is recursive formula?

A recursive formula is a formula that defines any tern of a sequence in terms ofits preceding term(s).

Now the given series is-

2,7/2,5,13/2,......

Here the the first term of the series is 2

⇒a₁ = 2

Common difference (d) = (7/2) - 2 = 3/2

Now the recursive formula of an arithmatic sequence is given as,

aⁿ = aⁿ⁻¹ + d

Putting the values,

aⁿ = aⁿ⁻¹ + 3/2

Hence,the recursive formula for the arithmatic sequence is a₁ = 2, aⁿ = aⁿ⁻¹ + 3/2.

More about recursive formula :

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