Chapter 11, Problem 2CR

To determine

To calculate:

The correct option which shows fifth term of this sequence $8,5,2,-1,\mathrm{....}$

  $\begin{array}{l}a.-2\\ b.-3\\ c.-4\\ d.-5\end{array}$

Answer to Problem 2CR

The correct option is (c).

The fifth term of this sequence is $-4$ .

Explanation of Solution

Given information:

  $\begin{array}{l}{a}_1=8\\ a_2=5\\ a_3=2\\ a_4=-1\end{array}$

Formula used:

Common ratio: $d=a_n-a_{n-1}$

Arithmetic progression: $a_n=a+\left(n-1\right)d$

Calculation:

Consider the following sequence:

  $\begin{array}{l}d=a_2-a_1=5-8=-3\\ d=a_3-a_2=2-5=-3\\ d=a_4-a_5=-1-2=-3\end{array}$

Apply the formula of arithmetic progression:

  $a_n=a+\left(n-1\right)d$

Put the values in the formula:

  $\begin{array}{l}{a}_5=a+\left(n-1\right)d\\ a_5=8+\left(5-1\right)\left(-3\right)\\ a_5=8+\left(-12\right)\\ a_5=-4\end{array}$

The correct option is (c).

The fifth term of this sequence is $-4$ .