Chapter 12: Q 46. (page 809)

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.
$a_{1} = - 1; a_{2} = 1; a_{n} = a_{n - 2} + n a_{n - 1}$

Short Answer

Expert verified

The first five terms of the recursively defined sequence are $- 1, 1, 2, 9, and 47$ .

Step by step solution

Step 1. Write the given information.

The given recursively defined sequence is:

$a_{1} = - 1 a_{2} = 1 a_{n} = a_{n - 2} + n a_{n - 1}$

Step 2. Determine the first and second terms and find out the third term.

The first term is $(a_{1}) = - 1$ .

The second term islocalid="1646734892458" $(a_{2}) = 1$

Now substitute 3 for nin the given formula $a_{n} = a_{n - 2} + n a_{n - 1}$ to get the third term,

$a_{3} = a_{3 - 2} + 3 a_{3 - 1} = a_{1} + 3 a_{2} = (- 1) + 3 (1) = 2$

Step 3. Find the 4th and 5th terms.

Similarly substitute 4 and 5 for nin the given formula to get the fourth and fifth term,

$a_{4} = a_{4 - 2} + 4 a_{4 - 1} = a_{2} + 4 a_{3} = 1 + 4 (2) = 9 a_{5} = a_{5 - 2} + 5 a_{5 - 1} = a_{3} + 5 a_{4} = 2 + 5 (9) = 47$

Therefore, the first five terms are $- 1, 1, 2, 9, 47$ .

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In Problems 37–50, a sequence is defined recursively. Write down the first five terms.
$a_{1} = - 1; a_{2} = 1; a_{n} = a_{n - 2} + n a_{n - 1}$

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Determine the first and second terms and find out the third term.

Step 3. Find the 4th and 5th terms.

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In Problems 37–50, a sequence is defined recursively. Write down the first five terms.a1=-1;a2=1;an=an-2+nan-1

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Determine the first and second terms and find out the third term.

Step 3. Find the 4th and 5th terms.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Logic and Functions

Applied Mathematics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems 37–50, a sequence is defined recursively. Write down the first five terms.
$a_{1} = - 1; a_{2} = 1; a_{n} = a_{n - 2} + n a_{n - 1}$