Chapter 13, Problem 1RE

Write the first four terms of the sequence defined by the recursive formula $a_1=2,a_n=a_{n-1}+n$.

To determine

The first four terms of the sequence.

Answer to Problem 1RE

The first four terms of the sequence are $2,4,7\text{ and }11$

Explanation of Solution

Given: The given sequence is defined by recursive formula $a_1=2,a_n=a_{n-1}+n$ .

Concept Used:

We use the concept of values. We put the values for $n$ in $a_n$ corresponding to the term we need to find.

Calculation:

As given $a_1=2,a_n=a_{n-1}+n$ , thus we already have our first term.

Now for second term we put $n=2$ and get $a_2=a_1+2=2+2=4$

  $\begin{array}{l}n=3,a_3=a_2+3=4+3=7\\ n=4,a_4=a_3+4=7+4=11\end{array}$

Conclusion:

The first four terms of the sequence are $2,4,7\text{ and }11$ .