Chapter SH, Problem 3.15EP

To determine

To find n^th term of the arithmetic sequence $3,3.5,4,4.5\mathrm{......}.$

Answer to Problem 3.15EP

  $a_n=0.5n+2.5$

  $a_5=5$

Graph:

  

Explanation of Solution

Given information:

The sequence $3,3.5,4,4.5\mathrm{......}.$

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 $3,3.5,4,4.5\mathrm{......}.$

  $First\text{ term, }{a}_1=3$

  $\text{Second term, }{a}_2=3.5$

Then,

Common difference is given below

  $d=3.5-3$

On solving,

  $d=\mathrm{0.5.}$

Then,

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

  $a_n=3+(n-1)0.5$

So,

  $=3+0.5n-0.5$

On solving,

  0.5n+2.5

Substituting n=5 in equation 0.5n+2.5 to find 5^th term of the sequence

Then,

  $a_n=0.5n-2.5$

On solving,

  $a_5=5$

Graph of the first five terms of the sequence $\{3,3.5,4,4.5,\mathrm{5....}\}$

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

  $(1,3)(2,3.5)(3,4)(4,4.5)(5,5)$