Chapter SH, Problem 3.16EP

To determine

To find n^th term of the arithmetic sequence $1,-1.5,-4,-6.5\mathrm{......}.$

Answer to Problem 3.16EP

  2.5n+3.5

  9

Graph:

  

Explanation of Solution

Given information:

The sequence $1,-1.5,-4,-6.5\mathrm{......}.$

Formula used:

  $a_n=a+(n-1)d$

d is common difference of the arithmetic sequence

where as,

  is the n^th term of the arithmetic sequence

a is first term in arithmetic sequence

And,

d is common difference of the arithmetic sequence

Calculation:

The sequence $1,-1.5,-4,-6.5\mathrm{......}.$

  $First\text{ term, }{a}_1=1$

  $\text{Second term, }{a}_2=-1.5$

Then,

Common difference is given below

  $d=-1.5-1$

On solving,

  $d=-\mathrm{2.5.}$

Then,

Substituting value of a and d in formula to calculate the n^th term of the arithmetic sequence

  $a_n=1+(n-1)(-2.5)$

So,

  $=1-2.5n+2.5$

On solving,

  $a_n=-2.5n+3.5$

Substituting $n=5$ in equation $a_n=-2.5n+3.5$ to find 5^th term of the sequence

Then,

  $a_5=-2.5(5)+3.5$

On solving,

  m:math display='block'>a5=-9

Graph of the first five terms of the sequence $\{1,-1.5,-4,-6.5,-9\mathrm{......}\}$

The sequence can be written as a set of oredered pairs where the first coordinate is the position of the term in the sequence and the second coordinate is the term

  $(1,1)(2,-1.5)(3,-4)(4,-6.5)(5,-9)$