Chapter 12: Q 103. (page 811)

A triangular number is a term of the sequence $u_{1} = 1, u_{n + 1} = u_{n} + (n + 1)$
Write down the first seven triangular numbers.

Short Answer

Expert verified

The first seven triangular numbers are $1, 3, 6, 10, 15, 21, and 28$ .

Step by step solution

Step 1. Write the given information.

The given triangular terms are:

$u_{1} = 1, u_{n + 1} = u_{n} + (n + 1)$

Step 2. Find the second and third triangular numbers.

The first triangular number is:

$u_{1} = 1$

The second and third triangular terms are:

$u_{2} = u_{1} + (1 + 1) = 1 + 2 = 3 u_{3} = u_{2} + (2 + 1) = 3 + 3 = 6$

Step 3. Find the fourth and fifth triangular numbers.

$u_{4} = u_{3} + (3 + 1) = 6 + 4 = 10 u_{5} = u_{4} + (4 + 1) = 10 + 5 = 15$

Step 4. Find the 6th and 7th triangular numbers.

$u_{6} = u_{5} + (5 + 1) = 15 + 6 = 21 u_{7} = u_{6} + (6 + 1) = 21 + 7 = 28$

Therefore the first seven triangular numbers are $1, 3, 6, 10, 15, 21, and 28$ .

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A triangular number is a term of the sequence $u_{1} = 1, u_{n + 1} = u_{n} + (n + 1)$
Write down the first seven triangular numbers.

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Find the second and third triangular numbers.

Step 3. Find the fourth and fifth triangular numbers.

Step 4. Find the 6th and 7th triangular numbers.

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A triangular number is a term of the sequence u1=1,un+1=un+n+1Write down the first seven triangular numbers.

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Find the second and third triangular numbers.

Step 3. Find the fourth and fifth triangular numbers.

Step 4. Find the 6th and 7th triangular numbers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Statistics

Probability and Statistics

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

A triangular number is a term of the sequence $u_{1} = 1, u_{n + 1} = u_{n} + (n + 1)$
Write down the first seven triangular numbers.