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Chapter 12: Q 103. (page 811)

A triangular number is a term of the sequence u1=1,un+1=un+n+1

Write down the first seven triangular numbers.

Short Answer

Expert verified

The first seven triangular numbers are1,3,6,10,15,21,and28.

Step by step solution

01

Step 1. Write the given information.

The given triangular terms are:

u1=1,un+1=un+n+1

02

Step 2. Find the second and third triangular numbers.

The first triangular number is:

u1=1

The second and third triangular terms are:

u2=u1+1+1=1+2=3u3=u2+2+1=3+3=6

03

Step 3. Find the fourth and fifth triangular numbers.

u4=u3+3+1=6+4=10u5=u4+4+1=10+5=15

04

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

u6=u5+5+1=15+6=21u7=u6+6+1=21+7=28

Therefore the first seven triangular numbers are1,3,6,10,15,21,and28.

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