Chapter 11.3, Problem 27WE

To determine

To calculate: The n^th term.

Answer to Problem 27WE

The general term for the sequence of positive even integers is $a_n=2n$ .

Explanation of Solution

Given information: The sequence of positive even integers Hence, the sequence is $2,4,6,8,10,\mathrm{...................}$

From the above sequence the common difference between the two terms are constant. Therefore, the given sequence is an Arithmetic Progression (A.P).

Let, first term, $a_1$ = 2

Second term, $a_2$ = 4

Third term, $a_3$ = 6

As we know that, the common difference, $d=a_2-a_1=a_3-a_2$

Now,

  $\begin{array}{l}\Rightarrow d=4-2=6-4\\ \Rightarrow d=2=2\end{array}$

Formula used: The n^th term of an Arithmetic Progression (A.P) is $a_n=a+\left(n-1\right)d$

Calculation:

  $\begin{array}{l}\Rightarrow a_n=2+\left(n-1\right)2\\ =2+2n-2\\ =2n\end{array}$

The general term for the sequence of positive even integers is given by $a_n=2n$ , where $n=1,2,3,4,\mathrm{............}$

Hence, the n^th term of an Arithmetic Progression (A.P) is 2n .