Math Problem Statement

Find a_(3). a_(1)=28 a_(n)=(1)/(2)a_(n-1) Write your answer as an integer or fraction in simplest form. a_(3)=

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Solution

We are given the recursive sequence formula:

a1=28a_1 = 28 an=12an1a_n = \frac{1}{2} a_{n-1}

We need to find a3a_3.

Step 1: Find a2a_2

Using the recursive formula with n=2n = 2:

a2=12a1=12×28=14a_2 = \frac{1}{2} a_1 = \frac{1}{2} \times 28 = 14

Step 2: Find a3a_3

Now, using the recursive formula with n=3n = 3:

a3=12a2=12×14=7a_3 = \frac{1}{2} a_2 = \frac{1}{2} \times 14 = 7

So, the value of a3a_3 is:

a3=7a_3 = 7

Would you like any further explanation?

Related Questions:

  1. What would a4a_4 be in this sequence?
  2. Can you express ana_n explicitly as a function of nn?
  3. How does this recursive formula compare to geometric sequences?
  4. What happens if the initial term a1a_1 was different, say a1=32a_1 = 32?
  5. Can this sequence reach zero at any value of nn?

Tip: Recursive formulas require the value of previous terms, so it's helpful to compute terms sequentially.

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Math Problem Analysis

Mathematical Concepts

Recursive Sequences
Algebra

Formulas

a_n = (1/2) * a_(n-1)

Theorems

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Suitable Grade Level

Grades 7-9