Recursive Sequences Calculator

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Example

Created on 2024-06-20Asked by Layla Roberts (Solvelet student)

Find the first five terms of the recursive sequence defined by:

b_0 = 2, \quad b_{n+1} = 2b_n + 1.

Solution

To find the first five terms of the recursive sequence defined by

b_0 = 2

and

b_{n+1} = 2b_n + 1

: 1. **Calculate the first term:**

b_0 = 2.

2. **Calculate the second term:**

b_1 = 2b_0 + 1 = 2 \cdot 2 + 1 = 5.

3. **Calculate the third term:**

b_2 = 2b_1 + 1 = 2 \cdot 5 + 1 = 11.

4. **Calculate the fourth term:**

b_3 = 2b_2 + 1 = 2 \cdot 11 + 1 = 23.

5. **Calculate the fifth term:**

b_4 = 2b_3 + 1 = 2 \cdot 23 + 1 = 47.

Therefore, the first five terms of the sequence are

2, 5, 11, 23, 47

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Owen Lee on Solvelet

1. Generate the first five terms of the Fibonacci sequence defined by the recurrence relation

F_n = F_{n-1} + F_{n-2}

with

F_0 = 0

and

F_1 = 1

.2. Find the general term of the geometric sequence defined by the recurrence relation

a_n = 2a_{n-1}

with

a_0 = 5

DefinitionA recursive sequence is a sequence that is specified by a relation that each expression in the sequence to those before it. They are defined a set of initial conditions and a recurrence relation be used to form the relationship between terms of the sequence. For example: the sequence is recursive a_n = 2*a_n − 1 + 3, a_0 = 1. First, they consist of geometric concepts of similarity and congruency.

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