Chapter 12.2, Problem 39E

To determine

Calculate the first three terms of an arithmetic sequence having $100thterm=98$ and common difference is $2$ .

Answer to Problem 39E

The first three term of the arithmetic is $-100,-98\&-96$ .

Explanation of Solution

Given information:

It is given in the question that,

  $100thterm=98$ and common difference is $2$ .

Formula used:

  $a_n=a+(n-1)d$

Where,

  $\begin{array}{l}aisthe{1}^{st}term\\ nisthenumberofterm\\ disthecommondifference\end{array}$

Calculation:

It is given in the question that $100thterm=98$ means,

  $a+99d=98$

And also given that common difference is $2$ means,

  $d=2$

By putting the value of $d$ in the above equation then,

  $\begin{array}{l}a+99*2=98\\ a=98-198\\ a=-100\end{array}$

So, $a_1=-100$

For finding the second and third term use formula $a_n=a+(n-1)d$ by putting $n=2,3$

For $n=2$ ,

  $\begin{array}{l}{a}_n=a+(n-1)d\\ a_2=-100+(2-1)*2\\ =-100+(1)*2\\ =-100+2\\ =-98\end{array}$

For $n=3$ ,

  $\begin{array}{l}{a}_n=a+(n-1)d\\ a_3=-100+(3-1)*2\\ =-100+(2)*2\\ =-100+4\\ =-96\end{array}$

Finally, $a_1=-100,a_2=-98,a_3=-96$