Chapter 4, Problem 13CT

To determine

To determine the second, fourth and eleventh terms of the sequence.

Answer to Problem 13CT

Second, fourth and eleventh terms of the sequence are respectively

  $-0.5,-5.5,-23$ .

Explanation of Solution

Given:

Explicit formula is

  $A\left(n\right)=2+\left(n-1\right)\left(-2.5\right)$

Calculation:

  $A\left(n\right)=2+\left(n-1\right)\left(-2.5\right)\mathrm{.......}\left(1\right)$

Since $n^{th}$ term of the arithmetic sequence with first term ‘a’ and common difference ‘d’ is given by

  $A\left(n\right)=a+\left(n-1\right)d\mathrm{......}\left(2\right)$

On Comparing both equations

  $a=2$ and $d=-2.5$

For second term, put $n=2$ in equation $\left(1\right)$

  $\begin{array}{l}A\left(2\right)=2+\left(2-1\right)\left(-2.5\right)\\ =2-2.5\\ =-0.5\end{array}$

For fourth term, put $n=4$ in equation $\left(1\right)$

  $\begin{array}{l}A\left(4\right)=2+\left(4-1\right)\left(-2.5\right)\\ =2-3\times 2.5\\ =2-7.5\\ =-5.5\end{array}$

For eleventh term, put $n=11$ in equation $\left(1\right)$

  $\begin{array}{l}A\left(11\right)=2+\left(11-1\right)\left(-2.5\right)\\ =2-10\times 2.5\\ =2-25\\ =-23\end{array}$