Chapter 3, Problem 49SGR

To determine

The next three terms of the given arithmetic sequence.

Answer to Problem 49SGR

The next three terms of the given arithmetic sequence are 64, 55, and 46.

Explanation of Solution

Given information:The arithmetic sequence given 100, 91, 82, 73...

Calculation:

The arithmetic sequence given 100, 91, 82, 73…

The common difference of the sequence is

  $d=a_2-a_1=91-100=-9$

Here given, first term $a_1=3$ ,

Second term:

  $a_2=a_1+d=100+(-9)=100-9=91$ .

Third term:

  $a_3=91+(-9)=91-9=82$ ,

Fourthterm:

  $a_4=82+(-9)=82-9=73$ .

Fifth term:

  $a_5=73+(-9)=73-9=64$

Sixth term:

  $a_6=64+(-9)=64-9=55$

Seventh term:

  $a_7=55+(-9)=55-9=46$

  $\therefore$ The next three terms are 64, 55, and 46.